Question

If two adjacent vertices of a parallelogram are (3,2) and (-1,0) and the diagonals intersect at (2, -5) then find the coordinates of the other two vertices.

Answer 1

We know that the midpoint of a line formed by two points is given by,

$(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$

Now, E is the midpoint of line AC,

$(2,-5)=(\frac{x_1+3}{2},\frac{y_1+2}{2})\frac{x_1+3}{2}=2|\frac{y_1+2}{2}=-5x_1+3=4|y_1+2=-10x_1=1|y_1=-12$

Now, E is the midpoint of line BD,

$(2,-5)=(\frac{x_2-1}{2},\frac{y_2+0}{2})\frac{x_2-1}{2}=2|\frac{y_2}{2}=-5x_2-1=4|y_2=-10x_2=5|y_2=-10$

The vertices are (1,-12) and (5,-10)