given W(-1,5), X(6,-2) an Y(-2,-7) find the co-ordinate of the point if WXYZ is a parallelogram

Question

it is a vectors question needed to be solved by using the dot product

Answer 1

Given the coordinates of a parallelogram W(-1,5),x(6,-2)Y(-2,-7)

Let missing coordinate  Z = (x,y)

In given parallelogram WX is parallel to YZ.

Now the vector WX is (6+1,-2-5) = (7,-7)

And now YZ is (x-7,y+7)

We know that parallelogram parallel sides are equal.

So x-7 = 7              and         y+7 = -7

Add 7 to each side.  and   subtract 7 from each side.

x-7+7 = 7+7         and      y+7-7 = -7-7

x = 14                  and      y = -14

Z(14,-14).