Question

The coordinates of the 3 of the vértices of a parallelogram are (-7, 3), (-6, 1), and (-4, 5). What is the equation for the line containing the side opposite the side containing the first two vertices?

Answer 1

We know, opposite sides are parallelogram is parallel, therefore slopes are equal.

Slope of line one :

$m=\dfrac{-7-(-6)}{3-1}\\\\m =\dfrac{-1}{2}\\\\m= -0.5$

So, equation of other line passing through (-4,5) and have slope of -0.5 is :

y-5 = -0.5( x-(-4))

y-5 = -0.5x - 2

y  + 1/2x = 3

2y + x = 6

Therefore, equation of line containing the (-4, 5) is 2y + x = 6.

Hence, this is the required solution.