Question

the vertices of a triangle PQR are P(-2,3), Q(2,1), R(4,5). Find the equation of altitude through R​

Answer 1

Given:-

• the vertices of a triangle PQR are P(-2,3), Q(2,1), R(4,5).

To find:-

• Find the equation of altitude through R

Solutions:-

• It is given that the vertices of ∆PQR are P(-2,3), Q(2,1), R(4,5).

• Let RL be the median through vertex R.

According,

L is the mid - point of PQ.

By mid - point formula, the coordinates of point L are given by (2 - 2 /2 , 1 + 3 /2) = (0, 2)

The equation of the line passing through points (x1, y1) and (x2, y2) is.

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

Therefore,

The equation of RL can be determined by substituting (x1, y1) = (4, 5) and (x2, y2) = (0, 2)

=> y - 5 = 2 - 5 / 0 - 4 (x - 4)

=> y - 5 = -3/-4 (x - 4)

=> 4(y - 5) = 3(x - 4)

=> 3x - 4y - 12 + 20 = 0

=> 3x - 4y + 8 = 0

Hence, the required equation of the median through vertex R is 3x - 4y + 8 = 0.