Chapter E, Problem 14.5EX

To determine

To choose: The correct option for the image of $\left(-1,3\right)$ by a half-turn about the point $\left(1,2\right)$ .

Answer to Problem 14.5EX

The correct option is (a).

Explanation of Solution

Given information: The center of rotation is $\left(1,2\right)$ . Rotate the point $\left(-1,3\right)$ by a half-turn.

Half-turn is $180°$ rotation of point in clock-wise direction.

Half turn have the point that is opposite to given point $\left(-1,3\right)$ from the center point $\left(1,2\right)$ and the same distance. The point will be:

  $\left(1-\left(-1\right),2-3\right)=\left(2,-1\right)$

The image of given point after the half-turn is:

  $\left(1+2,2-1\right)=\left(3,1\right)$

Therefore, the correct option is (a).