Question Bank: Coordinate Geometry

What are the coordinates of a point on the y-axis?

If point A has coordinates (2, 3) and point B has coordinates (5, 7), what is the distance between points A and B?

Which of the following equations represents a horizontal line in the Cartesian plane?

What is the x-coordinate of the point (0, -6)?

For the points P(3, 4) and Q(7, 1), find the slope of the line passing through them.

Which pair of points lie on the same vertical line?

What is the midpoint of points (6, 8) and (2, 4)?

If point A is at (0, 0) and point B is at (5, 12), what is the distance from A to B?

Which points have the same y-coordinate?

The distance between points A(0, 0) and B(3, 3) is equal to?

If point C divides the line segment between A(2, 4) and B(10, 8) in the ratio 1:3, what are the coordinates of C?

Identify the point that does NOT lie in the first quadrant.

What is the equation of a vertical line that passes through point (5, 3)?

What points are generally referred to as the origin in the Cartesian plane?

What are the coordinates of the point that divides the line segment joining (2, 3) and (8, 7) in the ratio 2:1?

Which point divides the segment connecting (0, 0) and (6, 9) in the ratio 1:2?

If a point divides the line segment joining (1, 2) and (5, 6) in the ratio 3:1, what are the coordinates of this point?

In what ratio does the point (-2, 3) divide the segment joining the points (0, 1) and (4, 5)?

What is the external division ratio if the point (3, 2) divides the segment from (1, 5) to (5, 1)?

If the mid-point of a segment is (4, 2), what are the coordinates of the points connecting it if they divide the segment in the ratio 1:1?

The coordinates of A and B are (3, 5) and (7, 9). What is the coordinate of P if it divides AB in the ratio 3:2 internally?

How does the point (1, 1) divide the segment connecting (1, 6) and (1, -4) internally?

Given A(2, 3) and B(6, 7), what ratio must a point P lie on segment AB such that its x-coordinate is 4?

What is the ratio of division when point (1, 2) lies on the line extending (1, 6) to (3, 8)?

If two points A(0, 2) and B(8, 6) are connected, what are the coordinates if point P divides AB in the ratio 4:1?

A line segment from P to Q has endpoints at (2, -3) and (4, 1). What is the coordinate of point R that divides the segment in the ratio of 1:2?

In the coordinate system, what point (x, y) divides (10, 5) and (20, 15) in the ratio 3:7?

What is the formula to find the centroid of a triangle given vertices A(x1, y1), B(x2, y2), and C(x3, y3)?

The centroid of a triangle divides each median in what ratio?

Consider a triangle with vertices at A(0, 0), B(6, 0), and C(3, 6). What are the coordinates of its centroid?

What does it mean for three points to be collinear?

Which of the following represents the centroid of a triangle formed by the points A(1, 4), B(3, 4), and C(1, 6)?

Which of the following sets of points is collinear?

What is the formula to calculate the area of a triangle formed by three points A(x1, y1), B(x2, y2), and C(x3, y3)?

How does the position of the centroid change if the three vertices of the triangle are all moved towards the positive quadrant?

If points A(1, 2), B(3, 6), and C(k, 10) are collinear, what is the value of k?

If the vertices of triangle ABC are A(1, 2), B(4, 6), C(7, 1), what is its area?

For vertices (x1, y1), (x2, y2), (x3, y3), what can be said about the centroid's coordinates if all vertex y-coordinates are equal?

What equation represents the line passing through the points (2, 3) and (4, 7)?

Which set of points is necessary to determine the area of a triangle in a coordinate plane?

Which of the following points would make the centroid of triangle A(1, 1) and B(4, 1) lie at (2.5, 1)?

Which of the following does NOT indicate collinear points?

Points P(1, 1), Q(3, 5), and R(5, 2) form what type of triangle?

A triangle is formed with vertices at A(2, 2), B(8, 2), and C(5, 6). What type of triangle is formed based on its centroid?

If A(2, 3), B(4, k), and C(6, 7) are collinear, what is the value of k?

How does the area of triangle ABC change if the height is doubled while the base remains the same?

Which triangle does not form if points A(1, 1), B(2, 2), and C(3, 3) are plotted?

If a triangle has vertices A(0, 0), B(b, 0), and C(b/2, h), what is its area?

Using the section formula, which point divides the segment AB(1, 2)(4, 6) in the ratio 1:2?

To verify if points A(-1, 2), B(3, 4), and C(5, k) are collinear, which calculation must be performed?

Find the area of triangle with vertices A(-2, 1), B(2, 3), C(4, -1).

If three points have the coordinates (2, 4), (k, 4), and (6, 4), what value of k ensures collinearity?

What is the area of a triangle formed by points (2, 3), (4, 5), and (6, 9)?

Vertices of a triangle are B(0, 0), C(4, 0), and A(4, 3). What is the area?

For points A(0, 0), B(0, 1), and C(1, 1), how can their collinearity be determined?

If triangle ABC has vertices A(2, 1), B(x, 5), C(8, 3), find x if the area equals 10.

What ratio does the point (3, 5) divide the segment joining A(1, 1) and B(5, 9)?

Given points A(-1, 0), B(0, 1), and C(1, 0), what type of triangle do they form?

If the points (5, 1), (k, 7), and (3, 5) are collinear, what is k?

The midpoint formula divides segment AB at what ratio?

What is the x-coordinate of point A located at (4, 5)?

What is the y-coordinate of the point B(7, -2)?

Using the distance formula, what is the distance between points (1, 1) and (4, 5)?

Which of the following point pairs is collinear?

What is the midpoint of the line segment joining (2, 3) and (4, 7)?

If point P(4, y) is equidistant from points A(1, 2) and B(7, 6), what is y?

Which equation is represented by the line joining points (1, 2) and (3, 4)?

What is the distance between points (0, 0) and (36, 15)?

How do you find the coordinates of the point that divides the line segment joining (1, 2) and (3, 4) in the ratio 2:3?

If point Q(0, 1) is equidistant from P(5, -3) and R(x, 6), what is the value of x?

How many points on the y-axis are equidistant from (6, 5) and (−4, 3)?

If points (−2, −2) and (2, −4) are joined, what is the midpoint?

What is the x-coordinate of the point A(5, 3)?

If a point is at (0, 7) on a coordinate plane, what is its y-coordinate?

What is the distance between the points (2, 0) and (5, 0) on the x-axis?

What is the distance between points (1, 1) and (4, 5)?

Which point lies in the fourth quadrant?

If the coordinates of point A are (3, 4) and of point B are (7, 1), what is the midpoint of segment AB?

Which equation represents a line parallel to the x-axis?

What type of coordinate system uses two perpendicular axes?

What is the result of the distance between points (x1, y1) and (x2, y2) using the distance formula?

If the coordinates of point C are (-2, -3) and of point D are (2, 3), what is the distance between them?

How many quadrants are there in a Cartesian coordinate system?

How can you represent a vertical line on a coordinate plane?

What is the slope of a line parallel to the y-axis?

Which of the following points lies at the origin of the coordinate system?

What is the distance between points A(2, 3) and B(5, 7)?

Find the distance between points P(1, -1) and Q(-2, 2).

What is the distance from point (0, 0) to point (x, y)?

Two points A(4, 0) and B(6, 0) lie on the x-axis. What is the distance between them?

The points C(1, 2) and D(4, 6) form what type of triangle with the origin?

What is the distance between points E(3, 3) and F(3, 7)?

Determine the distance between the points (1, 1) and (4, 5).

Find the value of y such that the distance between the points (2, -3) and (10, y) is 10 units.

Which of the following points is at a distance of 5 from the origin?

The distance from point A(x1, y1) to point B(x2, y2) is represented as:

Which of the following points is equidistant from (2, -1) and (5, 2)?

Given points R(4, 3) and S(4, 7), what is their distance apart?

If A(1, 1) and B(4, 5) are endpoints of a segment, and point C is the midpoint, what is the distance from C to the origin?

A point P(x, y) is equidistant from points A(7, 1) and B(3, 5), which equation describes this relationship?

The distance between the points (1, 2) and (-2, -1) is:

What is the coordinate of a point located on the y-axis?

What is the distance between the points A(2, 3) and B(5, 7)?

If point P(4, 5) and Q(6, y) are such that the distance PQ is 2 units, what is the value of y?

Which of the following points is not on the x-axis?

For which values of x and y does the point (x, y) lie on the line x + y = 8?

Which of the following pairs of coordinates form a right-angled triangle?

What is the midpoint of the segment joining A(2, 3) and B(4, 7)?

How do you find the coordinates of a point dividing the line segment joining A(3, 1) and B(9, 7) in the ratio 1:2?

If P(3, 2), Q(5, y) make a line that passes through the origin, find y.

What is the equation of the line that passes through (1, 2) and has slope 3?

The points (3, 4), (3, 4) and (3, 2) form what type of geometric figure?

Which of the following points lie in the fourth quadrant?

If A(1, 2) and B(-3, 4) are endpoints, what is the length of segment AB?

How to determine if three points are collinear?

What are the coordinates of the mid-point of the line segment joining (2, 4) and (10, 8)?

If a point P divides the segment joining points A(1, 2) and B(5, 6) in the ratio 1:3, what are the coordinates of point P?

What is the ratio in which the point (3, 5) divides the line segment joining the points (1, 1) and (5, 9)?

Using the section formula, what will be the coordinates of point P that divides the line segment joining (10, 20) and (30, 40) externally in the ratio 2:3?

What does a point dividing a line segment externally imply about the distance from each endpoint?

Calculate the coordinates of the point that divides the line segment joining (-3, 2) and (5, 10) in the ratio 1:1.

A point Q divides the segment joining (2, 3) and (4, 7) in the ratio 3:1. What is the y-coordinate of Q?

What is the section formula used to find the coordinates of a point that divides a segment internally?

If point R divides the segment from (5, 5) to (10, 10) in the ratio 2:3 internally, what are the coordinates of R?

Which of the following statements about the midpoint and section formula is correct?

Find the coordinates of the point that divides the segment joining (1, -1) and (2, 3) in the ratio 1:2.

If point D is at (2, 2), and it divides AB where A(1, 1) and B(7, 7) are endpoints, find the ratio in which D divides AB.

Determine the coordinates of point P that divides the line segment from (-1, -2) to (3, 4) externally in a ratio of 3:2.

How do the coordinates of a point that divides a segment externally differ from those that divide it internally?

What is the formula for the area of a triangle given its vertices (x1, y1), (x2, y2), (x3, y3)?

If a triangle has vertices at (2, 1), (4, 5), and (6, 2), what is its area?

Which of the following sets of points form a right triangle?

What is the area of the triangle with vertices at A(0, 0), B(6, 0), and C(3, 6)?

Which condition indicates that three points A, B, and C are collinear?

If the vertices of a triangle are (-5, 0), (0, 5), and (5, 0), what is the area?

Determine the height of a triangle with base length 10 units and area 30 square units.

Two vertices of a triangle are A(2, 3) and B(4, 7). If the base AB is 5 units long, what is the possible y-coordinate of the third vertex if the area should be 10 square units?

Which of the following points does NOT form a triangle with the origin (0,0)?

Find the area of a triangle with vertices (1,2), (4,2), and (4,5).

Given the coordinates of a triangle change from (x1, y1), (x2, y2) to new coordinates (x1 + 2, y1 + 2), (x2 + 2, y2 + 2). What happens to the area of the triangle?

What will be the area of a triangle formed by the points (5,5), (5,0), and (0,0)?

If the vertices of a triangle are at (2, 3), (4, 5), and (2, 7), what is the type of triangle?

Points (0,0), (2,2), (3,3) are known. Which statement is correct?

Which of the following points are collinear?

What is the section formula used for?

If points A, B, and C are (1,1), (2,2), and (3,4) respectively, are they collinear?

Point P(3, y) divides the segment AB joining A(1, 1) and B(5, 5) in the ratio 1:3. What is y?

The points A(2, 3), B(4, 5), and C(6, 7) lie on which type of path?

Find the ratio in which the point (2, 3) divides the line segment joining A(0, 2) and B(4, 6).

Which method can determine if points A(2, 4), B(4, 8), and C(6, 11) are collinear?

How do we find if three points A(x1, y1), B(x2, y2), C(x3, y3) are collinear?

A(1, 2), B(3, 6), and C(5, 8) are to be tested for collinearity. What must be true for successful affirmation?

What is the coordinate of the point that divides the segment from P(2, 3) to Q(8, 9) in the ratio 1:2?

What can be inferred if the determinant formed by three points results in zero?

Determine if the points (4, 4), (5, 6), and (7, 8) are collinear.

Points A(1, 1), B(2, 3), and C(3, 2) are placed in a cartesian plane. Determine their type of arrangement.

The point D(3, 3) divides the segment AB at A(2, 0) and B(x, 6) in the ratio 1:2. What is x?

What is the formula to find the centroid of a triangle with vertices at points A(x1, y1), B(x2, y2), and C(x3, y3)?

If the vertices of a triangle are A(2, 4), B(6, 8), and C(10, 2), what are the coordinates of the centroid?

The vertices of a triangle are A(1, 2), B(3, 4), and C(5, 2). Which of the following points represents the centroid?

If the centroid of triangle ABC is at (3, 3), and two vertices are A(1, 2) and B(5, 4), what are the coordinates of vertex C?

In a triangle, if the coordinates of the centroid are known as (a, a), and the triangle's vertices A(0, 0), B(a, 0), and C(a, a) are given, how can one describe the triangle?

Which of the following correctly describes a property of the centroid in relation to the median of a triangle?

If a triangle has vertices A(2, 3), B(4, 1), and C(0, 5), what is the total distance from each vertex to the centroid?

For a triangle with vertices A(2, 1), B(3, 4), and C(5, 4), which of the following statements is true regarding the centroid?

If triangle XYZ has vertices X(1, 2), Y(4, 6), Z(7, 2), what is the y-coordinate of the centroid?

In triangle PQR, the centroid G divides line segment PQ in what ratio?

Given the vertices of triangle DEF as D(0, 0), E(0, 6), and F(8, 0), identify the centroid's location.

What is a key characteristic of the centroid of a triangle?

Which of the following statements is true about the centroid of a triangle?