Question

triangle fgh has vertices f (-3, 4), g (2, 0), and h (-1, -2). triangle fgh is rotated 90° clockwise about g. in which quadrant is the image of point f?
a) quadrant i
b) quadrant ii
c) quadrant iii

Explanation:

Step1: Translate the points

Translate \( G(2,0)\) to the origin. Subtract \( (2,0)\) from \( F(-3,4)\): \( (-3 - 2,4 - 0)=(-5,4)\).

Step2: Rotate the translated point

A \(90^{\circ}\) clockwise rotation rule for a point \((x,y)\) is \((x,y)\to(y,-x)\). For \((-5,4)\), after rotation: \((4,5)\).

Step3: Translate back

Add \( (2,0)\) to \((4,5)\): \((4 + 2,5+0)=(6,5)\).

Answer:

A. Quadrant I