Question

The endpoints of AB are A(4,3) and B(1,1). What are the coordinates of A’’ after the image has been translated (x,y)—> (x-5,y-1) and rotated 180 degrees about the origin?

Answer 1

A"(1, -2)

Explanation:

In addition to the translation transformation given, you are asked to transform the figure further by rotating it 180° about the origin. The translation for that is ...

(x, y) ⇒ (-x, -y)

Then the composition of the two transformations is ...

(x, y) ⇒ (-(x -5), -(y -1)) = (-x +5, -y +1)

__

Applied to the given point(s), we have ...

(x, y) ⇒ (-x +5, -y +1)

A(4, 3) ⇒ (-4 +5, -3 +1) = A"(1, -2)

B(1, 1) ⇒ (-1 +5, -1 +1) = B"(4, 0)

The coordinates of A" after translation and rotation are (1, -2).