Question

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

what is the image of $(-6,9)$ after a reflection over $y$-axis?

1. what is the image of $(7,8)$ after a reflection over the line $y=-x$?
2. what is the image of $(-8,2)$ after a reflection over the $y$-axis?

Explanation:

Step1: Reflection over the y - axis rule

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\). For the point \((-7,-2)\), when we apply the rule, we change the sign of the \(x\) - coordinate.

Step2: Calculate the new coordinates

Given \(x=-7\) and \(y = - 2\), after reflection over the \(y\) - axis, the new \(x\) - coordinate is \(-x=-(-7) = 7\) and the \(y\) - coordinate remains \(y=-2\).

Answer:

\((7,-2)\)