Question

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:

Step1: Find original vertices

From the graph, the original vertices are \((-3,4)\), \((-4,-2)\), \((5,-3)\).

Step2: Apply reflection rule

The rule for reflection over the line \(y = x\) is \((x,y)\to(y,x)\).
For \((-3,4)\): \((-3,4)\to(4,-3)\)
For \((-4,-2)\): \((-4,-2)\to(-2,-4)\)
For \((5,-3)\): \((5,-3)\to(-3,5)\)

Answer:

The vertices of the reflected triangle are \((4, - 3)\), \((-2,-4)\), \((-3,5)\)