Question

Which of the following transformations maps A to A’ in the figure below

Answer 1

A rotation of 90° about the origin.

Explanation:

If you observe carefuly, notice that point A is next to y-axis, at the right side of the axis. Now observe that A' is right next to x-axis, at the right side if you put the North above the x-axis.

This transformation can be achieved by rotating around the origin 90°, a better way to deduct that is drawing a vertical line intercepting point A, and drawing a horizontal line intercepting point A'. You will notice that these lines are perpendicular each other.

Therefore, the right answer here is the first choice: A rotation of 90° about the origin.

Answer 2

The answer is rotation 270° about the origin

Explanation:

If (x , y) is a point in xy-coordinates

If the point rotate about the origin ⇒ (The positive direction is anti-clockwise)

1- 90°

Its image is (-y , x)

2- 180°

Its image is (-x , -y)

3- 270°

Its image is (y , -x)

If we assume A is (1 , 7)

1- ⇒ (-7 , 1) ⇒ rotation 90° about the origin

2- ⇒ (-1 , -7) ⇒ rotation 180° about the origin

3- ⇒ (7 , -1) ⇒ rotation 270° about the origin

∵ x-coordinate of point A small and +ve and y-coordinate large and +ve

∵ x-coordinate of point A' large and +ve and y-coordinate small and -ve

∴ The answer is rotation 270° about the origin

∴ The answer is rotation 270° about the origin