Question

1. the vertices of $\triangle abc$ are $a(-5, 4)$, $b(-2, 4)$, and $c(-4, 2)$. if $\triangle abc$ is reflected across the $y$-axis, find the coordinates of the vertex $c$.

Explanation:

Step1: Recall reflection over y - axis rule

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

Step2: Apply the rule to point \(C\)

Given the coordinates of point \(C\) are \((-4,2)\). Here, \(x = - 4\) and \(y = 2\).
Using the reflection rule, we substitute \(x=-4\) into \(-x\). So, \(-x=-(-4) = 4\) and \(y\) remains \(2\).

Answer:

The coordinates of \(C'\) are \((4,2)\)