Chapter 7.2, Problem 1QR

Solution

a.

To determine: The coordinates of the reflected points, which reflected across the given line.

  $\left(3,-2\right)$

The obtained point is $\left(3,2\right)$ .

Given Information:

The coordinate point is $\left(3,-2\right)$ .

Explanation:

Consider the given matrix,

If something is flipped over the $x$ -axis, the $x$ -coordinate sign doesn't change but the $y$ coordinate is change with the negative sign.

So, the reflected point over the $x$ -axis is defined as,

  $\left(3,-2\right)\underrightarrow{x-\text{axis}}\left(3,2\right)$

Therefore, the obtained points is $\left(3,2\right)$ .

a.

To determine: The coordinates of the reflected points, which reflected across the given line.

  $\left(x,y\right)$

The obtained point is $\left(x,-y\right)$ .

Given Information:

The coordinate point is $\left(x,y\right)$ .

Explanation:

Consider the given matrix,

If something is flipped over the $x$ -axis, the $x$ -coordinate sign doesn't change but the $y$ coordinate is change with the negative sign.

So the reflected point over the $x$ -axis is defined as,

  $\left(x,y\right)\underrightarrow{x-\text{axis}}\left(x,-y\right)$

Therefore, the obtained points is $\left(x,-y\right)$ .