Question

Rectangle ABCD has vertices at (-7,-2); (1, -2); (1, -8); and (-7, -8) respectively. If GHJK is a similar rectangle where G(2, 5) and H(6, 5); where could points J and K be located? Group of answer choices

Answer 1

Points J and K could be located at:

J(2,2)

K(6,2)

Explanation:

Consider the vertices have a x and y coordinate:

A: x coordinate=-7 y coordinate=-2

B: x coordinate=1 y coordinate=-2

C: x coordinate=1 y coordinate=-8

D: x coordinate=-7 y coordinate=-8

G: x coordinate=2 y coordinate=5

H: x coordinate=6 y coordinate=5

Then it is possible to calculate the distance between the x and y coordinates:

x coordinate of Vertices AB:

x coordinate of B- x coordinate of A=1-(-7)=8

The distance between A and B is 8

y coordinate of Vertices AC:

y coordinate of A- y coordinate of C=-2-(-8)=6

The distance between A and C is 6

Then we know that the side AB of Rectangle ABCD measures 8 and the side AC, measures 6.

Repeat the analysis with Rectangle GHJK. In this case, is only possible to calculate the distance with x coordinate.

x coordinate of Vertices GH:

x coordinate of H- x coordinate of G=6-(2)=4

The distance between G and H is 4

We can see that the distance in x of the Rectangle ABCD is 8, and the distance in x of the Rectangle GHJK is 4, it means that the measure of ABCD is twice GHJK.

Then, if the distance in y coordinate of Vertices AC is 6, we could say that the distance in y coordinate of Vertices GJ is 3.

Points J and K could be located at:

J(2,2)

K(6,2)