Choose three non-collinear points on the coordinate plane, making sure none of your points is the origin. On a sheet of paper, graph the three points and draw line segments to connect the points and make a triangle. Label the vertices of the triangle A, B, and C. Now describe the new coordinates of points A, B, and C after the following transformations: Translation of point A around the origin 90° rotation around point B Reflection of the triangle across the x-axis

I chose the next points:

A(1, 1)

B(2, 3)

C(3,2)

In the picture attached, the triangle is shown.

Translation of point A to the origin

The new triangle is:

A'(0, 0)

B(2, 3)

C(3,2)

90° rotation around point B

90°counter-clockwise rotation about the origin transforms (x, y) into (-y, x)

90°counter-clockwise rotation around a point  (2,3) is doing as follows: subtract the point, rotate around origin, add the point back:

A(1,1) → (-1, -2) → (2, -1) → A'(4, 2)

C(3,2) → (1, -1) → (1, 1) → C'(3,4)

The new triangle is:

A'(4, 2)

B(2, 3)

C'(3,4)

Reflection of the triangle across the x-axis

Reflection across x-axis transforms (x, y) into (x, -y). Then:

A(1, 1) → A'(1, -1)

B(2, 3) → B'(2, -3)

C(3,2) → C'(3,-2)