Triangle XYZ has vertices at X(−5, −5), Y(2, 2), Z(2, −4).Part A: If triangle XYZ is rotated 90° counterclockwise about the origin, determine the coordinates of the vertices for the image, triangle X′Y′Z′. (4 points)Part B: If triangle XYZ is rotated 270° clockwise about the origin, determine the coordinates of the vertices for the image, triangle X′Y′Z′. (4 points)Part C: Describe the similarities and differences between your answers to parts A and B. (4 points)

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28-10-2022
Mathematics

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Triangle XYZ has vertices at X(−5, −5), Y(2, 2), Z(2, −4).Part A: If triangle XYZ is rotated 90° counterclockwise about the origin, determine the coordinates of the vertices for the image, triangle X′Y′Z′. (4 points)Part B: If triangle XYZ is rotated 270° clockwise about the origin, determine the coordinates of the vertices for the image, triangle X′Y′Z′. (4 points)Part C: Describe the similarities and differences between your answers to parts A and B. (4 points)

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HaywardA638228 HaywardA638228 · Answer 1 · 2022-10-28T05:47:05+02:00

To find:

A. X'Y'Z' when the triangle is rotated 90 degrees counterclockwise.

B. X'Y'Z' when the triangle is rotated 270 degrees clockwise.

C. What is the similiarity in the points from part A and part B.

Solution:

The Triangle XYZ has vertices at X(−5, −5), Y(2, 2), Z(2, −4).

A. It is known that the point (x, y) becomes (-y, x) when it is rotated 90 degrees counterclockwise.

So, the point X(-5, -5) becomes X'(5, -5).

the point Y(2, 2) becomes Y'(-2, 2).

the point Z(2, -4) becomes Z'(4, 2)

So, the coordinates of the vertices of the triangle are X'(5, -5), Y'(-2, 2), Z'(4, 2).

B. It is known that point (x, y) becomes (-y, x) when it is rotated 270 clockwise.

So, the point X(-5, -5) becomes X'(5, -5).

the point Y(2, 2) becomes Y'(-2, 2).

the point Z(2, -4) becomes Z'(4, 2)

So, the coordinates of the vertices of the triangle are X'(5, -5), Y'(-2, 2), Z'(4, 2).

C. Here, the coordinates of the triangle after rotation of 90 degrees counterclockwise is same as the coordinates after rotation of 270 degrees clockwise.