Question

ii. graph the polygon

1. given a triangle, \\( \triangle efg \\) with the following vertices \\( (1,3) \\), \\( (4,1) \\) and \\( (3,5) \\), rotate at \\( 90^{\circ} \\) about the region. (3 pts)

Explanation:

Step1: Recall the rotation formula

When rotating a point \((x,y)\) \(90^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by the formula \(x'=-y\) and \(y' = x\).

Step2: Apply the formula to each vertex

• For the vertex \((1,3)\):

Substitute \(x = 1\) and \(y=3\) into the formula.
\(x'=-3\) and \(y'=1\), so the new vertex is \((-3,1)\).

• For the vertex \((4,1)\):

Substitute \(x = 4\) and \(y = 1\) into the formula.
\(x'=-1\) and \(y'=4\), so the new vertex is \((-1,4)\).

• For the vertex \((3,5)\):

Substitute \(x = 3\) and \(y = 5\) into the formula.
\(x'=-5\) and \(y'=3\), so the new vertex is \((-5,3)\).

Answer:

The vertices of the rotated triangle are \((-3,1)\), \((-1,4)\) and \((-5,3)\)