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QUESTION: 1

The value of y, for the line passing through (3, y) and (2, 7) is parallel to the line passing through (-1 , 4) and (0, 6) is:

Solution:

As A(3,y) and B(2,7) is parallel to C(-1,4) and D(0,6)

∴ their slopes are equal

so, (y-7)/(3-1) = (4-6)/(-1-0)

y-7 = 2

y=9

QUESTION: 2

The tangent of the angle which the part of the line above the X-axis makes with the positive direction of the X-axis is:

Solution:

The gradient or slope of a line (not parallel to the axis of y) is the trigonometrical tangent of the angle which the line makes with the positive direction of the x-axis. Thus, if a line makes an angle θ with the positive direction of the x-axis, then its slope will be tan θ.

QUESTION: 3

Two lines are said to be parallel when the difference of their slopes is

Solution:

Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope and lines with the same slope are parallel.

QUESTION: 4

m_{1 }and m_{2} are the slope of two perpendicular lines, if

Solution:

If the lines are perpendicular to each other then their slopes are in the form m1.m2 = -1

QUESTION: 5

The points A and B have coordinates (3, 2) and (1, 4) respectively. So, the slope of any line perpendicular to AB is

Solution:

If the lines are perpendicular to each other then their slopes are in the form m1.m2 = -1.(since product of slopes of two perpendicular lines is -1) Therefore , m = 1.

QUESTION: 6

Slope of a line is not defined, when q = ……

Solution:

Since tan θ is not defined when θ = 90°, therefore, the slope of a vertical line is not defined. i.e., slope of y-axis is m = tan 90° = ∞ i.e., not defined.

QUESTION: 7

If the slope of the line passing through the points (2, 5) and (x, 1) is 2, then x = ……

Solution:

Slope=change in y coordinates÷change in x coodinates

= (5-1)÷2-x=2

5-1=4-2x

0=2x

x=0

QUESTION: 8

If the slope of line m = tan 0°. Therefore, the line is …… to the X-axis.

Solution:

Slope of x-axis is m = tan 0° = 0.

Since the inclination of every line parallel to x-axis is 0°, so its slope (m) = tan 0° = 0. Therefore, the slope of every horizontal line is 0.

QUESTION: 9

If A (-2, 1), B (2, 3) and C (-2, -4) are three points, find the angle between the straight lines AB and BC.

Solution:

Let the slope of the line AB and AC are m_{1} and m_{2 }respectively.

Then,

Let θ be the angle between AB and BC. Then,

QUESTION: 10

Let A(2, 12) and B(6,4) be two points. The slope of a line perpendicular to the line AB is:

Solution:

Slope of the points A and B is -2 and the lines are perpendicular then

m1×m2 = -1.

∴ the slope is 1/2

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