Question

1. △cde with vertices c(-... c(6, -3), d(1, -1), and e(5, 3), using coordinates 12. naveen plotted his triangular garden on a coordinate plane. what are the vertices of the image of his garden if it is reflected in the line y = x?

Explanation:

To find the image of the triangular garden with vertices \( C(6, -3) \), \( D(1, -1) \), and \( E(5, 3) \) when reflected over the line \( y = x \), we use the reflection rule for a point \((a, b)\) over the line \( y = x \), which is \((a, b) \to (b, a)\).

Step 1: Reflect Vertex \( C(6, -3) \)

For the point \( C(6, -3) \), applying the reflection rule \( (a, b) \to (b, a) \):
\( a = 6 \), \( b = -3 \), so the image is \( (-3, 6) \).

Step 2: Reflect Vertex \( D(1, -1) \)

For the point \( D(1, -1) \), applying the reflection rule \( (a, b) \to (b, a) \):
\( a = 1 \), \( b = -1 \), so the image is \( (-1, 1) \).

Step 3: Reflect Vertex \( E(5, 3) \)

For the point \( E(5, 3) \), applying the reflection rule \( (a, b) \to (b, a) \):
\( a = 5 \), \( b = 3 \), so the image is \( (3, 5) \).

Answer:

The image of the triangular garden has vertices \( C'(-3, 6) \), \( D'(-1, 1) \), and \( E'(3, 5) \).