Question

Bridget drew ΔYZ and Δ′ ′ ′ on a coordinate plane, as shown below.

Which statement about the relationship between ΔYZ and Δ′ ′ ′ is true?

A: Δ′ ′ ′ is NOT a translation of ΔXYZ because not all points contained in Δ′ ′ ′ have negative x-coordinates.

B: Δ′ ′ ′ is a translation of ΔXYZ because their corresponding sides are parallel.

C: Δ′ ′ ′ is a translation of ΔXYZ because all points in Δ′ ′ ′ are the same distance and direction from the corresponding points in ΔXYZ.

D: Δ′ ′ ′ is NOT a translation of ΔXYZ because the y-coordinate of Point is not the same as the y-coordinate of point ′.

Answer 1

The statement that is true about the relationship between ΔXYZ and ΔX'Y'Z' is option "C"

C. ΔX'Y'Z' is a translation of ΔXYZ because all points in ΔX'Y'Z' are the same distance and direction from the corresponding points in ΔXYZ

Explanation:

The triangles Bridget drew are;

ΔXYZ and ΔX'Y'Z'

The coordinates of ΔXYZ = X(-5, 7), Y(-9, 2), Z(-3, 2)

The coordinates of ΔX'Y'Z' = X'(1, 2), Y'(-3, -3), Z'(3, -3)

From the coordinates we have;

The x-coordinates of ΔX'Y'Z' = The x-coordinates of ΔXYZ + 6

The y-coordinates of ΔX'Y'Z' = The y-coordinates of ΔXYZ - 5

Therefore, the translation that gives ΔX'Y'Z' from ΔXYZ = T₆, ₋₅

Therefore;

1) ΔX'Y'Z' is obtained from ΔXYZ by a translation as the points in ΔX'Y'Z' are obtained from ΔXYZ by adding the same value to the x-coordinates of the points on ΔXYZ and subtracting the same value to the y-coordinates of the points on ΔXYZ, such that the points in triangle ΔX'Y'Z' are equidistant from and on the same side relative to the corresponding points on ΔXYZ

2) Given that triangle ΔXYZ and ΔX'Y'Z' are not rotated or reflected, we have that the corresponding sides of ΔXYZ and ΔX'Y'Z' are parallel

The correct options are therefore option "C" and and the option "B" is only partially correct because the sides can be parallel but do not have the same size.