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.

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4

"exterior angles = 360 / number of sides.

60 = 360 / sides

sides = 360 / 60

sides = 6"