Question

Triangle XYZ with vertices X(4,-1), Y(8,-2), and Z(1,-8) rotate counterclockwise 180 degrees

Answer 1

To rotate the triangle XYZ counterclockwise 180 degrees, is X'(-4,-8), Y'(-8,-8), and Z'(1,1)

My apologies for the confusion in my previous response. There was an error in the calculations. Let's correct it:

To rotate a point counterclockwise 180 degrees using the rotation formula:

`\[ x' = x \cos(180^\circ) - y \sin(180^\circ) \]`

`\[ y' = x \sin(180^\circ) + y \cos(180^\circ) \]`

Applying the formula to the vertices X(4,-1), Y(8,-2), and Z(1,-8):

`\[ X' = 4 \cos(180^\circ) - (-1) \sin(180^\circ) = -4 + 0 = -4 \]`

`\[ Y' = 8 \cos(180^\circ) - (-2) \sin(180^\circ) = -8 + 0 = -8 \]`

`\[ Z' = 1 \cos(180^\circ) - (-8) \sin(180^\circ) = 1 + 0 = 1 \]`

Therefore, the corrected rotated triangle has vertices X'(-4,-8), Y'(-8,-8), and Z'(1,1).