Question

Point P'(-3, 2) is the image of point P(3, 8) under a translation. What is the image of (0, -6) under the

Answer 1

Answer:

The image of the point (0, -6) under the same translation is (-6, -12)

Step-by-step explanation:

Let us revise the rules 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)

∵ The coordinate of point P are (3, 8)

∵ The coordinates of its image P' are (-3, 2)

→ The x-coordinate is changed from 3 to -3, that means the point

   translated to the left by h units

∵ h = -3 - 3

∴ h = -6

→ The y-coordinate is changed from 8 to 2, that means the point

   translated down by k units

∵ k = 2 - 8

∴ k = -6

→ By using the rule above

∴ The rule of translation is (x, y) → (x - 6, y - 6)

∵ The coordinates of the point are (0, -6)

∴ The coordinates of its image are (0 - 6, -6 - 6)

∴ The coordinates of its image are (-6, -12)