Question

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

Answer 1

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.

Answer 2

Answer:

The correct option is A.

Step-by-step 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.