Question

enter the coordinates of the image after abcd is reflected across the y-axis.
abcd | abcd
a(-4,3) |?
b(-2,3) |?
c(-2,-1) |?
d(-4,-1) |?
image: graph of quadrilateral abcd on coordinate plane with y-axis, grid lines, points a, b, c, d labeled.

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: Find \(A'\)

For point \(A(-4,3)\), applying the reflection rule: \(x=-4\), so \(-x = 4\), \(y = 3\). Thus, \(A'(4,3)\).

Step3: Find \(B'\)

For point \(B(-2,3)\), applying the reflection rule: \(x=-2\), so \(-x = 2\), \(y = 3\). Thus, \(B'(2,3)\).

Step4: Find \(C'\)

For point \(C(-2,-1)\), applying the reflection rule: \(x=-2\), so \(-x = 2\), \(y=-1\). Thus, \(C'(2,-1)\).

Step5: Find \(D'\)

For point \(D(-4,-1)\), applying the reflection rule: \(x=-4\), so \(-x = 4\), \(y=-1\). Thus, \(D'(4,-1)\).

Answer:

\(A'(4,3)\), \(B'(2,3)\), \(C'(2,-1)\), \(D'(4,-1)\)