Question

A (1, 1)

B (2, 3)
C (5, 3)
Parallelogram ABCD has the coordinates shown.

Find the coordinates of point D.

Answer 1

D(4 ; 1)

Explanation:

vector(AB)=(2-1 ; 3-1) = (1 ; 2)

vector(DC)=(5-x ; 3-y) and D(x ; y )

ABCD parallelogram :vector(AB)=vector(DC)

you have the system : 5-x =1

3-y =2

so : x=4 and y=1

D(4 ; 1)

Answer 2

D(4, 1)

Explanation:

The two diagonals have the same midpoint, so ...

(A+C)/2 = (B+D)/2

A+C = B+D . . . . multiply by 2

A+C-B = D . . . . . subtract B

D = (1, 1) + (5, 3) - (2, 3) = (1+5-2, 1+3-3)

D = (4, 1)