If A(-2,-1), B (x,0), C (4,Y) and D (1,2) are the vertices of a parallelogram , taken in order, find x and y. also find the area of ABCD.

Question

If A(-2,-1), B (x,0), C (4,Y) and D (1,2) are the vertices of a parallelogram , taken in order, find x and y. also find the area of ABCD.

Answer 1

This was intended as a comment.

x = -1? y = 5?

A(-2, -1), B(-1, 0), C(4, 5), D(1, 2)

Is that a parallelogram?

Answer 2

We know that parallelograms have parallel opposite sides, which means that the slope of AB = CD and the slope of BC = AD.  Can you use this fact to set up some equations to solve for x and y? slope is change in y over change in x: slope of AB = (-1 - 0)/(-2 - x), which simplifies to 1/(x+2) slope of CD = (y-2)/3 slope of BC = y/(4-x) slope of AD = 1 slope of AB = CD so 1/(x+2) = (y-2)/3 OR (x+2)(y-2) = 3 slope of BC = AD so y/(4-x) = 1 OR y = 4-x we can substitute to get (x+2)(2-x) = 3 2x - x^2 +4 - 2x = 3 4 - x^2 = 3 x^2 = 1 x = 1 or -1 if x = 1, then y = 3 if x = -1 then y = 5 as Mark points out above, if x = -1 and y = 5, you get s straight line, so we can eliminate that answer.