Question

graph \\( \triangle a b c \\) and its image after a rotation \\( 90^{circ} \\) about the origin

Explanation:

Step1: Find coordinates of \(\triangle ABC\)

From the graph, \(A(-4,1)\), \(B(2,4)\), \(C(4,1)\)

Step2: Apply rotation rule

The rule for a \(90^{\circ}\) rotation about the origin \((x,y)\to(-y,x)\)

• For point \(A(-4,1)\): \(x = - 4,y = 1\), after rotation \(A'(-1,-4)\)
• For point \(B(2,4)\): \(x = 2,y = 4\), after rotation \(B'(-4,2)\)
• For point \(C(4,1)\): \(x = 4,y = 1\), after rotation \(C'(-1,4)\)

Step3: Graph the points

Plot \(A(-4,1)\), \(B(2,4)\), \(C(4,1)\) for \(\triangle ABC\) and \(A'(-1,-4)\), \(B'(-4,2)\), \(C'(-1,4)\) for the rotated triangle.

Answer:

Graph \(\triangle ABC\) with vertices \(A(-4,1)\), \(B(2,4)\), \(C(4,1)\) and its image (rotated \(90^{\circ}\) about the origin) with vertices \(A'(-1,-4)\), \(B'(-4,2)\), \(C'(-1,4)\)