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Flash Cards: Straight Lines

This chapter explores the properties and equations of straight lines in coordinate geometry, emphasizing their significance in mathematics and real-life applications.

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Straight Lines - Flash Cards

These flash cards cover important concepts from Straight Lines in Mathematics for Class 11 (Mathematics).

1/20

What is the distance formula between points P(x₁, y₁) and Q(x₂, y₂)?

1/20

The distance d(PQ) = √((x₂ - x₁)² + (y₂ - y₁)²).

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2/20

How do you find the midpoint of a line segment?

2/20

Midpoint coordinates: ((x₁ + x₂)/2, (y₁ + y₂)/2).

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3/20

What are the coordinates of a point dividing a line segment in the ratio m:n?

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3/20

Coordinates: ((m*y₂ + n*y₁)/(m+n), (m*x₂ + n*x₁)/(m+n)).

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4/20

What is the formula for the area of a triangle given its vertices?

4/20

Area = 1/2 | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |.

5/20

What defines the slope of a line?

5/20

Slope m = tan(θ), where θ is the inclination of the line with the x-axis.

6/20

How do you calculate the slope of a line given two points?

6/20

Slope m = (y₂ - y₁)/(x₂ - x₁) for points P(x₁, y₁) and Q(x₂, y₂).

7/20

When are two lines parallel in terms of slope?

7/20

Two lines are parallel if their slopes are equal: m₁ = m₂.

8/20

When are two lines perpendicular in terms of slope?

8/20

Two lines are perpendicular if m₁ * m₂ = -1.

9/20

How is the angle between two lines related to their slopes?

9/20

tan(θ) = (m₁ - m₂)/(1 + m₁*m₂) for lines with slopes m₁ and m₂.

10/20

What does an undefined slope indicate?

10/20

An undefined slope occurs in a vertical line (x = constant).

11/20

What does a zero slope indicate?

11/20

A zero slope indicates a horizontal line (y = constant).

12/20

What is the slope of the line through (3, –2) and (7, –2)?

12/20

Slope m = 0 (horizontal line).

13/20

What is the slope of the line through (3, –2) and (3, 4)?

13/20

Slope is undefined (vertical line).

14/20

What is the slope of a line with an inclination of 45°?

14/20

m = tan(45°) = 1.

15/20

What is the slope of a line with an inclination of 60°?

15/20

m = tan(60°) = √3.

16/20

What does it mean if the area of triangle formed by three points is zero?

16/20

The points are collinear.

17/20

What is the equation of a horizontal line?

17/20

y = c, where c is a constant.

18/20

What is the equation of a vertical line?

18/20

x = c, where c is a constant.

19/20

How does slope relate to the steepness of a line?

19/20

Higher |m| indicates steeper lines; m > 0 means upward slope, m < 0 means downward slope.

20/20

Where do we use slopes in real life?

20/20

Slope is used in architecture, roads, and physics to calculate inclines.

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