Question

Geometry:

The vertices of triangle ABC are A(0, 0), B(8, 1), and C(5, 5). Find the coordinates of the image of triangle ABC after a rotation of 90 degrees counterclockwise about the origin, a reflection over the x-axis, and a translation using the rule (x, y) → (x + 6, y - 1).

Answer 1

Explanation:

The transformations you want are ...

• 90° CCW: (x, y) ⇒ (-y, x)
• reflection over x-axis: (x, y) ⇒ (x, -y)
• translation by your rule: (x, y) ⇒ (x+6, y-1)

Taken together, these make the transformation ...

(x, y) ⇒ (-y+6, -x-1)

So, your points become ...

A(0, 0) ⇒ A'(6, -1)

B(8, 1) ⇒ B'(5, -9)

C(5, 5) ⇒ C'(1, -6)

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The attachment shows the original triangle in red and the progression to the final triangle in blue.