Question

Two quadrilaterals ABCD and EFGH are drawn on a coordinate grid. The coordinates of the vertices of each quadrilateral are given below.

ABCD : A(-8, 0), B(-3, 12), C(9, 7), D(3, -5)
EFGH : E(-7, 7), F(-2, 19), G(10, 14), H(4, 2)

Which statement about the two quadrilaterals is true?

ABCD has half the area of EFGH.

ABCD is twice as large as EFGH.

ABCD is congruent to EFGH.

ABCD is neither congruent nor similar to EFGH

Answer 1

do you notice anything when you compare the coordinates?

Answer 2

i dont have any graph paper :/

Answer 3

no no just look at the question. take E-A, F-B, G-C, H-D

Answer 4

they are almost the same numbers.. so they are similar

Answer 5

yea the second quadrilateral efgh is exact the same. it's just moved 1 to the right and 7 up (difference of x = 1, y = 7)

Answer 6

okay (:

Answer 7

That is what you are looking at (for the most part).

Answer 8

It can also be observed that there is a shift occurring here. (difference of x = 1, y = 7). So since the new shape has been formed only due to a shift on the coordinates (all together), the area has to be the same; showing signs of congruence.

Answer 9

ah, okay thankyou! :D