Question

1. examine the figure below, reflect the preimage across the x - axis, be sure to correctly label all points.

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ across the $x -$axis, the rule is $(x,y)\to(x, - y)$.

Step2: Find new coordinates of point A

Point A has coordinates $(0,-1)$. Using the reflection rule, the new coordinates of A' are $(0,1)$ since $x = 0$ and $y=-1$ becomes $-y = 1$.

Step3: Find new coordinates of point B

Point B has coordinates $(-3,-2)$. Using the reflection rule, for $x=-3$ and $y = - 2$, the new coordinates of B' are $(-3,2)$ as $-y=2$.

Step4: Find new coordinates of point C

Point C has coordinates $(-2,-4)$. Using the reflection rule, for $x=-2$ and $y=-4$, the new coordinates of C' are $(-2,4)$ as $-y = 4$.

Step5: Plot and label new points

Plot points A'$(0,1)$, B'$(-3,2)$ and C'$(-2,4)$ on the coordinate - plane and label them correctly.

Answer:

The new points after reflection across the x - axis are A'(0,1), B'(-3,2), C'(-2,4) and they should be plotted and labeled on the coordinate - plane.