Answer:
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
Step-by-step 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.
