SLOPE OF THE LINE PASSING THROUGH THE MIDPOINT OF THE LINE SEGMENT

In this section, you will learn how to find slope of a line passing through the midpoint of the line segment.

Example 1 :

Find the slope of the line which passes through the origin and the midpoint of the line segment joining the points (0 ,- 4) and (8 , 0).

Solution :

Midpoint of the line segment  =  (x₁ + x₂)/2, (y₁ + y₂)/2

  =  (0 + 8)/2, (-4 + 0)/2

  =  (8/2, -4/2)

  =  (4, -2)

Slope of the passing through the point (4, -2) and (0, 0) is

m  =  (y₂ - y₁)/(x₂ - x₁)

m  =  (0 + 2)/(0 - 4)

m  =  -2/4  =  -1/2

Example 2 :

The side AB of a square ABCD is parallel to x-axis . Find the

(i) slope of AB (ii) slope of BC (iii) slope of the diagonal AC

Solution :

(i)  Slope of AB

The side AB is parallel to x-axis, hence the slope of AB is 0.

(ii) slope of BC 

The side BC is perpendicular to x-axis, hence its slope is undefined.

(iii) slope of the diagonal AC

Angle of inclination of the diagonal AC is 45

m  =  tan 45

m  =  1

Example 3 :

The side BC of an equilateral Δ ABC is parallel to x-axis. Find the slope of AB and the slope of BC

Solution :

The side BC is parallel to x-axis, hence its slope is undefined.

Since it is right triangle the angle of inclination is 60

m  =  tan 60

m  =  √3

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