Question

graph (\triangle abc) with vertices (a(0,-2)), (b(0,-4)), and (c(-4,-1)) and its image after a (90^{circ}) rotation about the origin.

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the new point is \((-y,x)\).

Step2: Apply the rule to each vertex

• For \(A(0,- 2)\):

Substitute \(x = 0\) and \(y=-2\) into \((-y,x)\). We get \((2,0)\).

• For \(B(0,-4)\):

Substitute \(x = 0\) and \(y = - 4\) into \((-y,x)\). We get \((4,0)\).

• For \(C(-4,-1)\):

Substitute \(x=-4\) and \(y = - 1\) into \((-y,x)\). We get \((1,-4)\).

Answer:

The vertices of the image \(\triangle A'B'C'\) are \(A'(2,0)\), \(B'(4,0)\) and \(C'(1,-4)\).