Question

The vertices of a rectiſngle are R(-5, -5), S(-1,-5), T(-1, 1), and U(-5,1). A translation

maps R to the point (-4, 2). Find the translation rule and the image of U.

Answer 1

The translation rule is T (x, y) → (x + 1, y + 7)

The image of point U is (-4, 8)

Explanation:

Let us revise the rule of translation

• 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)

∵ Point R = (-5, -5)

∵ Point R' = (-4, 2)

∵ -4 > -5 and 2 > -5

→ That means point R translated to the right and up T (x, y) → (x + h, y + k)

∴ h = -4 - (-5) = -4 + 5 = 1 unit

∴ k = 2 - (-5) = 2 + 5 = 7 units

→ By using the 1st and 3rd rules above

∴ The translation rule is T (x, y) → (x + 1, y + 7)

∵ Point U = (-5, 1)

→ By using the rule of translation above

∴ U' = (-5 + 1, 1 + 7)

∴ U' = (-4, 8)

∴ The image of point U is (-4, 8)