Question

Given that P(3,4), Q(-5,1) and R(6,-7) are the vertices of a triangle. Find the equation of the line the midpoint of PQ parallel to PR

Answer 1

The equation -> y = -11x/3 - 7/6

The required line is parallel to the line PR . Therefore, the line will have slope equal to the line PR .

Slope of line PR = (x2 - x1)/(y2 - y1)

= (-7 - 4)/(6 - 3)

= -11/3

Slope of the required line = m= -11/3

The line passes through the midpoint of the line PQ .

Midpoint of PQ = ((3-5)/2 , (4+1)/2)

Midpoint = (-1 , 5/2) = (x1 , y1)

Equation of the required line -

y - y1 = m(x - x1)

=> y - 5/2 = -11/3 (x + 1)

=> y = -11x/3 - 7/6

The required equation of the line is

y = -11x/3 - 7/6