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 O.

Short answer

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

Step-by-step solution

a.Step 1. Given Information.

Coordinate of point O is $(0,0)$

Step 2. Explanation.

The image of O $(0,0)$ in the x-axis is $(0,0)$as the point lie in the line of reflection

Step 3. Conclusion.

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

b.Step 1. Given Information.

Coordinate of point O is $(0,0)$

Step 2. Calculation.

Image of O $(0,0)$in the y-axis is $(0,0)$ as the point pass through the y-axis.

Step 3. Conclusion.

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

c.Step 1. Given Information.

Coordinate of point O is $(0,0)$.

Step 2. Calculation.

The image of $(0,0)$ in the line $x=y$ is $(0,0)$as the point lie in the line of reflection.

Step 3. Conclusion.

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