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 A.

Short answer

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

Step-by-step solution

a.Step 1. Given Information.

Coordinate of A is $(2,4)$

Step 2. Explanation.

Reflection of $A=(2,4)$ in the x-axis is $(2,-4)$.

Step 3. Conclusion.

So, the image of A in the $x-\text{axis}$ is $(2,-4)$, $R_{x-axis}:A=(2,4)\to (2,-4)$

b.Step 1. Given Information.

Coordinate of A is $(2,4)$.

Step 2. Calculation.

Reflection of $A=(2,4)$ in the y-axis is $(2,-4)$.

Step 3. Conclusion.

So, $R_{y-axis}:A=(2,4)\to (-2,4)$.

c.Step 1. Given Information.

Coordinate of A is $(2,4)$.

Step 2. Calculation.

Reflection of $A=(2,4)$ in the line $y=x$ is $(4,2)$

Step 3. Conclusion.

Therefore, $R_{y=x}:A=(2,4)\to (4,2)$.