Answer:
vertex B' is at (1, 1)
Step-by-step explanation:
Let us revise the rules of translation of a point
- If the point (x, y) translated horizontally to the right by h units then its image is (x + h, y) ⇒ T (x, y) → (x + h, y)
- If the point (x, y) translated horizontally to the left by h units then its image is (x - h, y) ⇒ T (x, y) → (x - h, y)
- If the point (x, y) translated vertically up by k units then its image is (x, y + k)→ (x + h, y) ⇒ T (x, y) → (x, y + k)
- If the point (x, y) translated vertically down by k units then its image is (x, y - k) ⇒ T (x, y) → (x, y - k)
Let us use the rules to solve our question
∵ Vertex A = (-5, 2)
∵ Vertex A' = (2, -2)
→ The coordinates of the two points changed which means the
quadrilateral is translated horizontally and vertically
∵ The x-coordinate of A = -5
∵ The x-coordinate of A' = 2
→ Which means it moves to the right, so use the first rule above
∴ the rule of translation is T (x, y) → (x + h, y)
∴ x → x + h
∵ x = -5 and x + h = 2
∴ -5 + h = 2
→ Add 5 to both sides
∴ -5 + 5 + h = 2 + 5
∴ h = 7
∴ The quadrilateral is translated 7 units right
∵ The y-coordinate of A = 2
∵ The y-coordinate of A' = -2
→ Which means it moves down, so use the 4th rule above
∴ the rule of translation is T (x, y) → (x, y - k)
∴ y → y - k
∵ y = 2 and y - k = -2
∴ 2 - k = -2
→ Add K to both sides
∴ 2 - k + k = -2 + k
∴ 2 = -2 + k
→ Add 2 to both sides
∴ 2 + 2 = -2 + 2 + k
∴ 4 = k
∴ The quadrilateral is translated 4 units down
→ Let us find B'
∵ T (x, y) → (x + h, y - k) is the rule of translation
∵ B = (-6, 5)
∵ h = 7 and k = 4
∴ B' = (-6 + 7, 5 - 4)
∴ B' = (1, 1)
∴ vertex B' is at (1, 1)
