Question

Write the coordinates of the image of each point by reflection in,

1. The $x-axis$
2. The $y-axis$
3. The line $y=x$ (Hint: Refer to the Example on page 578)

Point E.

Short answer

1. $R_{x-axis}:E=(-3,-2)\to (-3,2)$
2. $R_{y-axis}:E=(-3,-2)\to (3,-2)$
3. $R_{y=x}:E=(-3,-2)\to (-2,-3)$

Step-by-step solution

a.Step 1. Given Information.

Coordinate of point E is $(-3,-2)$

Step 2. Explanation.

Image of E $(-3,-2)$ in the x-axis is

$(-3,2)$

Step 3. Conclusion.

So, the image of D in the $x-\text{axis}$is $R_{x-axis}:E=(-3,-2)\to (-3,2)$

b.Step 1. Given Information.

Coordinate of point E is $(-3,-2)$

Step 2. Calculation.

Image of $(-3,-2)$in the y-axis is $(3,-2)$

Step 3. Conclusion.

SO, $R_{y-axis}:E=(-3,-2)\to (3,-2)$.

c.Step 1. Given Information.

Coordinate of point E is $(-3,-2)$

Step 2. Calculation.

Image of $(-3,-2)$ in the line $x=y$ is $(-2,-3)$

Step 3. Conclusion.

Therefore, $R_{y=x}:E=(-3,-2)\to (-2,-3)$.