Question

the coordinates of a point and its image are given. is the reflection in the x-axis or y-axis? (2, -4) to (-2, -4) the coordinates of a point and its image are given. is the reflection in the x-axis or y-axis? (-9, -6) to (-9, 6)

Explanation:

First Sub - Question: Coordinates (2, - 4) to (-2, - 4)

To determine if a reflection is over the x - axis or y - axis, we use the rules of reflections. The rule for reflection over the y - axis is \((x,y)\to(-x,y)\), and the rule for reflection over the x - axis is \((x,y)\to(x, - y)\). For the points \((2,-4)\) and \((-2,-4)\), the x - coordinate changes sign (from \(2\) to \(- 2\)) and the y - coordinate remains the same (\(-4\) stays \(-4\)). This matches the rule for reflection over the y - axis \((x,y)\to(-x,y)\) (here \(x = 2\), so \(-x=-2\) and \(y=-4\)).

Using the reflection rules: For reflection over the x - axis, the rule is \((x,y)\to(x,-y)\), and for reflection over the y - axis, the rule is \((x,y)\to(-x,y)\). For the points \((-9,-6)\) and \((-9,6)\), the x - coordinate remains the same (\(-9\) stays \(-9\)) and the y - coordinate changes sign (from \(-6\) to \(6\)). This matches the rule for reflection over the x - axis \((x,y)\to(x,-y)\) (here \(x=-9\), \(y = - 6\), so \(-y = 6\)).

Answer:

The reflection is in the y - axis.

Second Sub - Question: Coordinates (-9, - 6) to (-9, 6)