What is the image of (1, -6) for a 180° counterclockwise rotation about the origin? a( -1,-6) b( -1,6) c(6,1) d( -6,-1)

option b

Step-by-step explanation:

It is important to know that, by definition, the rule for 180 degrees counterclockwise rotation is:

→

Therefore, given the point (1, -6) we can find the image obtained for  for a 180° counterclockwise rotation about the origin by applying the rule mentioned before.

Then, the image is:

 →

The correct answer option is b. ( -1, 6).

Step-by-step explanation:

We are given a point which is rotated 180 degrees counterclockwise about the origin (0, 0). We are to find the coordinates of the image of this point after the rotation.

The rule for rotating a point 180 degrees counterclockwise is:

(x, y) ---> (-x, -y)

So for the given point, the coordinates of the image will be:

(1, -6) ---> (-1, -(-6)) ---> (-1, 6)

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation:

cant see photo

step-by-step explanation: