Question

1. what is the image of (-7, -9) after a reflection over the x - axis? 23. what is the image of (-4, -2) after a reflection over the line y = -x?

Explanation:

Step1: Recall reflection rule over x - axis

The rule for reflecting a point $(x,y)$ over the x - axis is $(x,-y)$.
For the point $(-7, - 9)$, when reflected over the x - axis, the x - coordinate remains the same and the y - coordinate changes sign.

Step2: Apply the rule

The x - coordinate of $(-7,-9)$ is $x=-7$ and the y - coordinate is $y = - 9$. After reflection over the x - axis, the new y - coordinate is $-(-9)=9$. So the image is $(-7,9)$.

Step3: Recall reflection rule over the line $y=-x$

The rule for reflecting a point $(x,y)$ over the line $y =-x$ is $(-y,-x)$.
For the point $(-4,-2)$, when reflected over the line $y=-x$, we swap the x and y coordinates and change their signs.

Step4: Apply the rule

The x - coordinate of $(-4,-2)$ is $x=-4$ and the y - coordinate is $y=-2$. After reflection over the line $y=-x$, the new x - coordinate is $-(-2) = 2$ and the new y - coordinate is $-(-4)=4$. So the image is $(2,4)$.

Answer:

1. $(-7,9)$
2. $(2,4)$