Question Bank - Coordinate Geo...
Coordinate Geometry explores the relationship between algebra and geometry through the use of coordinate systems to represent geometric shapes and solve problems.
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?
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