## Equation of line Solution4

In this page equation of line solution4 we are going to see solution of each problem with detailed explanation of the worksheet slope of the line.

(8) Find the equation of the straight line passing through the points

(i) (-2 , 5) and (3 , 6)

Here we have two points on the straight line so we have to use the formula

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(y - 5)/(6 - 5) = (x - (-2))/(3 - (-2))

(y - 5)/(1) = (x + 2)/(3 + 2)

(y - 5) = (x + 2)/5

5 y - 25 = x + 2

x -  5 y + 25 + 2 = 0

x - 5 y + 27 = 0

(ii) (0 , -6) and (-8 , 2)

Here we have two points on the straight line so we have to use the formula

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(y - (-6))/(2 - (-6)) = (x - 0)/(-8 - 0)

(y + 6)/(2 + 6) = x/(-8)

(y + 6)/(8) = x/(-8)

y + 6 = - x

x + y + 6 = 0

(9) Find the equation of the median from the vertex R in a triangle PQR with vertices at P(1,-3),Q(-2,5) and R (-3 ,4)

Solution:

First let us draw a rough diagram for the given information.

To find equation of the median from the vertex R first we have to find the midpoint of the side PQ. Because the median always passes through the midpoint of the opposite side.

Midpoint = (x₁ + x₂)/2 ,(y₁ + y₂)/2

= (1-2)/2 , (-3+5)/2

= -1/2 , 2/2

= S (-1/2 , 1)

Now we can use two point form to find equation of the median RS

R(-3 , 4) S (-1/2 , 1)

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(y - 4)/(1 - 4) = (x - (-1/2))/[(-1/2) - (-3)]

(y - 4)/(- 3) = (x + (1/2))/[(-1+6)/2]

(y - 4)/(- 3) = (2x + 1)/(5/2)

(y - 4)/(- 3) = (2/5)(2x + 1)

5(- 3 y + 12) = 2 (2 x + 1)

-6 y + 60 = 4 x + 2

4 x + 6 y + 2 - 58 = 0

4 x + 6 y - 56 = 0

Divided by 2 we get, 2 x + 3 y - 28 = 0

9

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