Question

transformation: reflection

1. if triangle cde has vertices at c(-4, 3), d(-1, 4), and e(-2, 2) is reflected across ( y = x ), what are the coordinates for the image of triangle cde?

a. ( c(-4, -3) ), ( d(-1, -4) ), ( e(-2, -2) )
b. ( c(3, -4) ), ( d(4, -1) ), ( e(2, -2) )
c. ( c(-4, 3) ), ( d(1, 4) ), ( e(2, 2) )
d. ( c(-3, 4) ), ( d(-4, 1) ), ( e(-2, 2) )
e. ( c(3, 4) ), ( d(4, 1) ), ( e(2, -2) )

Explanation:

Step1: Recall reflection over \( y = x \) rule

The rule for reflecting a point \((x, y)\) across the line \( y = x \) is to swap the \( x \)-coordinate and the \( y \)-coordinate, so the image point is \((y, x)\).

Step2: Apply the rule to point \( C(-4, 3) \)

For \( C(-4, 3) \), swapping \( x \) and \( y \) gives \( C'(3, -4) \).

Step3: Apply the rule to point \( D(-1, 4) \)

For \( D(-1, 4) \), swapping \( x \) and \( y \) gives \( D'(4, -1) \).

Step4: Apply the rule to point \( E(-2, 2) \)

For \( E(-2, 2) \), swapping \( x \) and \( y \) gives \( E'(2, -2) \).

Answer:

B. \( \text{C}'(3, -4),\ \text{D}'(4, -1),\ \text{E}'(2, -2) \)