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 C.

Short answer

1. $R_{x-axis}:C=(0,-2)\to (0,2)$
2. $R_{y-axis}:C=(0,-2)\to (0,-2)$
3. $R_{y=x}:C=(0,-2)\to (-2,0)$

Step-by-step solution

a.Step 1. Given Information.

Coordinate of point C is $(0,-2)$.

Step 2. Explanation.

Image of $(0,-2)$ in the x-axis is $(0,2)$.

Step 3. Conclusion.

So, the image of C in the $x-axis$is $R_{x-axis}:C=(0,-2)\to (0,2)$

b.Step 1. Given Information.

Coordinate of point C is $(0,-2)$.

Step 2. Calculation.

Image of $(0,-2)$ in the y-axis is $(0,-2)$ as the point is on y-axis

Step 3. Conclusion.

So, $R_{y-axis}:C=(0,-2)\to (0,-2)$.

c.Step 1. Given Information.

Coordinate of point C is $(0,-2)$.

Step 2. Calculation.

Image of $(0,-2)$in the line $x=y$ is $(-2,0)$

Step 3. Conclusion.

Therefore, $R_{y=x}:C=(0,-2)\to (-2,0)$.