Answer:

Step-by-step explanation:
Method #1
We can draw a <em>right triangle</em> on the graph upon where the points are located and use the Pythagorean Theorem:





* Whenever we talk about distance, we ONLY want the NON-NEGATIVE root.
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Method #2
We can use the Distance Formula:
![\sqrt{[-x_1 + x_2]^{2} + [-y_1 + y_2]^{2}} = D](https://tex.z-dn.net/?f=%5Csqrt%7B%5B-x_1%20%2B%20x_2%5D%5E%7B2%7D%20%2B%20%5B-y_1%20%2B%20y_2%5D%5E%7B2%7D%7D%20%3D%20D)
<em>N</em>[−3, 2] <em>M</em>[−6, 0]
![\sqrt{[3 - 6]^{2} + [0 + 2]^{2}} = D](https://tex.z-dn.net/?f=%5Csqrt%7B%5B3%20-%206%5D%5E%7B2%7D%20%2B%20%5B0%20%2B%202%5D%5E%7B2%7D%7D%20%3D%20D)
![\sqrt{[-3]^{2} + 2^{2}} = D](https://tex.z-dn.net/?f=%5Csqrt%7B%5B-3%5D%5E%7B2%7D%20%2B%202%5E%7B2%7D%7D%20%3D%20D)


* Whenever we talk about distance, we ONLY want the NON-NEGATIVE root.
** You see? It does not matter which method you choose, as long as you are doing the work correctly.
I am delighted to assist you anytime.
The <u>correct answer</u> is:
B) A 90° counterclockwise rotation about the origin, followed by a reflection across the x-axis, followed by a translation 8 units right and 1 unit up.
Explanation:
The coordinates of the <u>points of the pre-image</u> are:
(3, 1)
(3, 4)
(5, 7)
(6, 5)
(6, 2)
The coordinates of the <u>points of the image</u> are:
(7,-2)
(4,-2)
(1,-4)
(3,-5)
(6,-5)
A 90° counterclockwise rotation about the origin negates the y-coordinate and switches it and the x-coordinate. Algebraically,
(x,y)→(-y,x).
When this is applied to our points, we get:
(3, 1)→(-1, 3)
(3, 4)→(-4, 3)
(5, 7)→(-7, 5)
(6, 5)→(-5, 6)
(6, 2)→(-2, 6)
A reflection across the x-axis negates the y-coordinate. Algebraically,
(x, y)→(x, -y).
Applying this to our new points, we have:
(-1, 3)→(-1, -3)
(-4, 3)→(-4, -3)
(-7, 5)→(-7, -5)
(-5, 6)→(-5, -6)
(-2, 6)→(-2, -6)
A translation 8 units right and 1 unit up adds 8 to the x-coordinate and 1 to the y-coordinate. Algebraically,
(x, y)→(x+8, y+1).
Applying this to our new points, we have:
(-1, -3)→(-1+8,-3+1) = (7, -2)
(-4, -3)→(-4+8,-3+1) = (4, -2)
(-7, -5)→(-7+8,-5+1) = (1, -4)
(-5, -6)→(-5+8,-6+1) = (3, -5)
(-2, -6)→(-2+8,-6+1) = (6, -5)
These match the coordinates of the image, so this is the correct series of transformations.