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 B.

Short answer

1. Image of B in the $x-axis$is $(4,0)$, $R_{x-axis}:B=(4,0)\to (4,0)$
2. $R_{y-axis}:B=(4,0)\to (-4,0)$
3. $R_{y=x}:B=(4,0)\to (0,4)$

Step-by-step solution

a.Step 1. Given Information.

Coordinate of point B is $(4,0)$.

Step 2. Explanation.

Image of B $(4,0)$in the x-axis is $(4,0)$. The image of point is itself as it is on the line in which the image is taken.

Step 3. Conclusion.

So, the image of B in the $x-axis$is $(4,0)$, $R_{x-axis}:B=(4,0)\to (4,0)$

b.Step 1. Given Information.

Coordinate of point B is $(4,0)$.

Step 2. Calculation.

Image of B $(4,0)$ in the y-axis is $(-4,0)$.

Step 3. Conclusion.

So, $R_{y-axis}:B=(4,0)\to (-4,0)$.

c.Step 1. Given Information.

Coordinate of point B is $(4,0)$.

Step 2. Calculation.

Image of B $(4,0)$ in the line $x=y$ is $(0,4)$

Step 3. Conclusion.

Therefore, $R_{y=x}:B=(4,0)\to (0,4)$.