Question

Harper draws a parallelogram with two pairs of parallel sides. Three of the vertices are shown below. What are the coordinates of the fourth vertex?

Answer 1

The coordinates from the graph are A(2,3), B(5, -3), C(-1, -5)

Let the coordiante of the fourth vertex be D(x, y)

Since AB is parallel and equal in lenght to CD, the transformation that maps B to A will be equal to the transformation that map C to D

B to A = ( 5-2, -3-3) = (3, -6)

To get the coordinate of D by mapping C to D by (3, -6)

We have

D(x, y ) = C(-1, -5) - (3, -6)

D(x, y) = (-1-3, -5-(-6) )

D(x, y)= (-4, -5+6)

D(x, y) = ( -4, 1)

Hence, the fourth coordinate is (-4, 1)