Question

complete the table to show the coordinates of △abc and its image.
△abc | △abc
a(-4,3) | ?
b(-2,1) | ?
c(-4,1) | ?

Explanation:

To solve for the coordinates of the image \(\triangle A'B'C'\) after a reflection (assuming a reflection over the \(y\)-axis, as the triangle is on the left of the \(y\)-axis and the image is likely on the right), we use the rule for reflecting a point \((x, y)\) over the \(y\)-axis: \((x, y) \to (-x, y)\).

Step 1: Find \(A'\)

For point \(A(-4, 3)\):
Using the reflection rule, \(x = -4\) becomes \(-(-4) = 4\), and \(y = 3\) remains.
Thus, \(A' = (4, 3)\).

Step 2: Find \(B'\)

For point \(B(-2, 1)\):
Using the reflection rule, \(x = -2\) becomes \(-(-2) = 2\), and \(y = 1\) remains.
Thus, \(B' = (2, 1)\).

Step 3: Find \(C'\)

For point \(C(-4, 1)\):
Using the reflection rule, \(x = -4\) becomes \(-(-4) = 4\), and \(y = 1\) remains.
Thus, \(C' = (4, 1)\).

Answer:

• \(A'\): \(\boldsymbol{(4, 3)}\)
• \(B'\): \(\boldsymbol{(2, 1)}\)
• \(C'\): \(\boldsymbol{(4, 1)}\)