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:

1. First, identify the original vertices of the triangle:

• Let's assume the original vertices of the triangle are \((x_1,y_1)\), \((x_2,y_2)\), and \((x_3,y_3)\). From the graph, if we assume the vertices are \((- 1,1)\), \((-1,4)\), and \((3,2)\) (by observing the grid - based on the position of the points relative to the \(x\) and \(y\) axes).

1. Recall the rule for reflection over the line \(y = x\):

• The rule for reflecting a point \((x,y)\) over the line \(y=x\) is \((x,y)\to(y,x)\).
• For the point \((-1,1)\):
• When we apply the reflection rule \((x,y)\to(y,x)\), the new point is \((1, - 1)\).
• For the point \((-1,4)\):
• Applying the rule \((x,y)\to(y,x)\), the new point is \((4,-1)\).
• For the point \((3,2)\):
• Applying the rule \((x,y)\to(y,x)\), the new point is \((2,3)\).

Answer:

The vertices of the reflected triangle are \((1,-1)\), \((4, - 1)\), and \((2,3)\)