Question

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 to produce the image $\triangle abc$, find the coordinates of the vertex $c$. the coordinates of $c$ are (type an ordered pair)

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 \(C\)

The coordinates of point \(C\) are \((-4,2)\). Using the reflection rule across the \(y\) - axis, we change the sign of the \(x\) - coordinate. So for \(x=-4\), the new \(x\) - coordinate is \(-(-4) = 4\), and the \(y\) - coordinate remains \(2\).

Answer:

\((4,2)\)