Question

The coordinates of 3 of the vertices of a parallelogram are (–3, 4), (–2, 1), and (2, 6). What is the equation for the line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a parallelogram are parallel.)

Answer 1

Given:
(-3,4) ; (-2,1) ; and (2,6)

let us solve for the slope. parallel sides have the same slope.

m = y2-y1 / x2-x1
m = 1 - 4 / -2-(-3)
m = -3 / 1
m = -3

y = mx + b
(2,6)
6 = -3(2) + b
6 = -6 + b
6 + 6 = b
12 = b

y = -3x + 12 This is the equation.