Question

Plot the points A(7,1), B(-2, 3), C(1, -7) on the coordinate axes below. State the

coordinates of point D such that A, B, C, and D would form a parallelogram.
(Plotting point D is optional.)

Answer 1

A B

D C

vectors

AB = DC

AB (-2-7 ; 3-1) => AB (-9 ; 2)

DC (1-x : -7-y)

1 - x = -9 => x = 10

-7-y = 2 => y = -9

D(10 ; -9)

Answer 2

D = (10, -9)

Explanation:

If ABCD is a parallelogram, then AB = DC and BC = AD

Therefore,

`\sf x_A-x_B=x_D-x_C`

`\sf \implies 7-(-2)=x_D-1`

`\sf \implies x_D=10`

`\sf y_A-y_B=y_D-y_C`

`\sf \implies 1-3=y_D-(-7)`

`\sf \implies y_D=-9`

Therefore, D = (10, -9)