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)

The correct option is A.

Step-by-step explanation:

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

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

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

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

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .