Question

the coordinates of a point and its image are given. is the reflection in the x-axis or y-axis? (3, −5) to (−3, −5) the coordinates of a point and its image are given. is the reflection in the x-axis or y-axis? (−8, −1) to (−8, 1)

Explanation:

First Sub - Question: Determine reflection for (3, - 5) to (- 3, - 5)

Step 1: Recall reflection rules

The rule for reflection over the \(y\) - axis is \((x,y)\to(-x,y)\), and the rule for reflection over the \(x\) - axis is \((x,y)\to(x, - y)\).

Step 2: Analyze the given points

For the points \((3,-5)\) and \((-3,-5)\), the \(x\) - coordinate changes from \(3\) to \(-3\) (i.e., \(x\to - x\)) and the \(y\) - coordinate remains the same (\(y=-5\) in both cases). This matches the rule for reflection over the \(y\) - axis \((x,y)\to(-x,y)\).

Second Sub - Question: Determine reflection for (- 8, - 1) to (- 8, 1)

Step 1: Recall reflection rules

Again, the rule for reflection over the \(y\) - axis is \((x,y)\to(-x,y)\), and the rule for reflection over the \(x\) - axis is \((x,y)\to(x, - y)\).

Step 2: Analyze the given points

For the points \((-8,-1)\) and \((-8,1)\), the \(x\) - coordinate remains the same (\(x = - 8\) in both cases) and the \(y\) - coordinate changes from \(-1\) to \(1\) (i.e., \(y\to - y\) since \(-(-1)=1\)). This matches the rule for reflection over the \(x\) - axis \((x,y)\to(x, - y)\).

Answer:

For the first pair \((3, - 5)\) to \((-3, - 5)\), the reflection is over the \(y\) - axis.
For the second pair \((-8, - 1)\) to \((-8, 1)\), the reflection is over the \(x\) - axis.