Chapter 7.2, Problem 3QR

Solution

a.

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

  $\left(3,-2\right)$

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

Given Information:

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

Explanation:

Consider the given matrix,

When the axis reflect a point across the line $y=x$ , the $x$ -coordinate and the $y$ -coordinate change places to each other.

  $\left(3,-2\right)\underrightarrow{y=x}\left(-2,3\right)$

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

a.

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

  $\left(x,y\right)$

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

Given Information:

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

Explanation:

Consider the given matrix,

When the axis reflect a point across the line $y=x$ , the $x$ -coordinate and the $y$ -coordinate change places to each other.

  $\left(x,y\right)\underrightarrow{y=x}\left(y,x\right)$

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