Question

What is the image of the point (–3, 4) after a rotation of 90° counterclockwise about the point (–3, 0)?

A.



(–7, 0)


B.



(1, 0)


C.



(0, –3)


D.



(–3, –4)

Answer 1

The correct option is A.

Explanation:

If a point rotated 90° counterclockwise about the point (a, b), then

`(x,y)\Rightarrow (-(y-b)+a,x-a+b)`

If a point rotated 90° counterclockwise about the point (–3, 0), then

`(x,y)\Rightarrow (-y-3,x+3)`

The coordinates of given point are (-3,4). So, the image of the point (–3, 4) after a rotation of 90° counterclockwise about the point (–3, 0) is

`(-3,4)\Rightarrow (-4-3,(-3)+3)`

`(-3,4)\Rightarrow (-7,0)`

The image of given point is (-3,4). Therefore the correct option is A.

Answer 2

Initially, the point (-3,4) is in the second quadrant of the cartesian plane. If the rotation is about point (-3,0) at 90 degrees, you find a point that when connected to (-3,4) makes two lines perpendicular to each other. Since the direction is counterclockwise, you move 3 points to the left, then 4 points down. That would be (-7,0). The answer is A.