Question

What is the image point of (7,-7) after a translation of 3 right and 1 down followed by

a reflection over the x-axis?

Answer 1

The image point of P(7,-7) after a translation of 3 right and 1 down followed by a reflection over the x-axis will be:

• P''(10, 8)

Explanation:

Given the point

(7, -7)

Translation of 3 right and 1 down means we need to add 3 units to the x-coordinate and subtract 1 unit from the y-coordinate

Therefore, the translation rule:

(x, y) → (x+3, y-1)

In our case, let the point P(7, -7)

P(7, -7) → P'(7+3, -7-1) → P'(10, -8)

FOLLOWED BY A reflection over the x-axis

We know that the rule of reflection over the x-axis implies that

(x y) → (x, -y)

i.e. the x-coordinate of the point remains the same, but the y-coordinate changes its sign.

After the first transformation, we had got P'(10, -8)

so

P'(10, -8) → P''(10, -(-8)) → P''(10, 8)

Therefore, the image point of P(7,-7) after a translation of 3 right and 1 down followed by a reflection over the x-axis will be:

• P''(10, 8)