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 point

Translate \(F(-3,4)\) and \(G(2,0)\) so that \(G\) is at the origin. Subtract the coordinates of \(G\) from \(F\): \((-3 - 2,4 - 0)=(-5,4)\).

Step2: Apply the \(90^{\circ}\) clockwise rotation formula

The formula for a \(90^{\circ}\) clockwise rotation of a point \((x,y)\) about the origin is \((y,-x)\). For the point \((-5,4)\), after rotation, it becomes \((4,5)\).

Step3: Translate back

Add the coordinates of \(G\) (which were subtracted in Step1) back to the rotated - translated point. \((4+2,5 + 0)=(6,5)\).

Answer:

A. Quadrant I