Answer:
5. The vertices of ΔX'Y'Z' are (-3, -7), (-6, -4), (-1, -2)
6. The vertices of ΔX'Y'Z' are (6, -7), (3, -4), (8, -2)
Step-by-step explanation:
If the point (x, y) translated by T → (h, k), then its image is (x + h, y + k)
#5
In ΔXYZ
∵ X = (1, -4), Y = (-2, -1), Z = (3, 1)
∵ T → (-4, -3)
∴ h = -4 and k = -3
→ Use the rule above to find the image of the vertices of the Δ
∵ X' = (1 + -4, -4 + -3)
∴ X' = (-3, -7)
∵ Y' = (-2 + -4, -1 + -3)
∴ Y' = (-6, -4)
∵ Z' = (3 + -4, 1 + -3)
∴ Z' = (-1, -2)
∴ The vertices of ΔX'Y'Z' are (-3, -7), (-6, -4), (-1, -2)
#6
In ΔXYZ
∵ X = (1, -4), Y = (-2, -1), Z = (3, 1)
∵ T → (5, -3)
∴ h = 5 and k = -3
→ Use the rule above to find the image of the vertices of the Δ
∵ X' = (1 + 5, -4 + -3)
∴ X' = (6, -7)
∵ Y' = (-2 + 5, -1 + -3)
∴ Y' = (3, -4)
∵ Z' = (3 + 5, 1 + -3)
∴ Z' = (8, -2)
∴ The vertices of ΔX'Y'Z' are (6, -7), (3, -4), (8, -2)
<em> congruent by SAS</em>
<em> congruent by corresponding theorem</em>
