Question

1. if the point (13, 10) were reflected using the x - axis as the line of reflection, what would be the coordinates of the image? what about (13, -20)? (13, 570)? explain how you know.

Explanation:

Step1: Recall reflection rule

When a point $(x,y)$ is reflected over the $x - axis$, the $x$-coordinate remains the same and the $y$-coordinate changes its sign. The rule is $(x,y)\to(x, - y)$.

Step2: Reflect point $(13,10)$

Applying the rule $(x,y)\to(x, - y)$ with $x = 13$ and $y=10$, we get $(13, - 10)$.

Step3: Reflect point $(13,-20)$

Applying the rule $(x,y)\to(x, - y)$ with $x = 13$ and $y = - 20$, we get $(13,20)$ since $-(-20)=20$.

Step4: Reflect point $(13,570)$

Applying the rule $(x,y)\to(x, - y)$ with $x = 13$ and $y = 570$, we get $(13,-570)$.

Answer:

The image of $(13,10)$ is $(13, - 10)$.
The image of $(13,-20)$ is $(13,20)$.
The image of $(13,570)$ is $(13,-570)$.