Question

Point P( 1, –1) is rotated 180°, then translated
( − 1, − 2).What is P′′?

Answer 1

P" = (-2, -1)

Explanation:

When a point P(x, y) is rotated 180° clockwise or anticlockwise the coordinates of the new point P'(x', y') become (-x, -y). The rotated point has coordinates which are negative of the original coordinates

When a point is translated (a, b) then new coordinates become (x + a,, y + b)

Here point P is (1, -1)

Rotation by 180° ⇒ rotated point P'(-1, 1)

If we translate P' by (-1, -2) translated point

P" has coordinates x" = -1 -1 = -2 and y" = 1 -2 = -1

So coordinates of P" are (-2, -1)