Question

1. 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 )? (original vertices: ( c(6, -3) ), ( d(1, -1) ), ( e(5, 5) ))

Explanation:

To determine the vertices of the image of a triangle reflected over the line \( y = x \), we use the reflection rule for a point \((a, b)\) over \( y = x \), which is \((a, b) \to (b, a)\).

Step 1: Identify the original vertices

From the problem (and assuming the original vertices are \( C(6, -3) \), \( D(1, -1) \), and \( E(5, 3) \) – since the image shows a triangle with these coordinates):

• Original vertex \( C \): \( (6, -3) \)
• Original vertex \( D \): \( (1, -1) \)
• Original vertex \( E \): \( (5, 3) \)

Step 2: Apply the reflection rule \( (a, b) \to (b, a) \) to each vertex

For \( C(6, -3) \):

Swap the \( x \)- and \( y \)-coordinates:
\( (6, -3) \to (-3, 6) \)

For \( D(1, -1) \):

Swap the \( x \)- and \( y \)-coordinates:
\( (1, -1) \to (-1, 1) \)

For \( E(5, 3) \):

Swap the \( x \)- and \( y \)-coordinates:
\( (5, 3) \to (3, 5) \)

Answer:

The vertices of the reflected triangle are \( C'(-3, 6) \), \( D'(-1, 1) \), and \( E'(3, 5) \).