Triangle XYZ has vertices X(1, –1), Y(3, 4), and Z(5, –1). Nikko rotated the triangle 90° counterclockwise about the origin. What is the correct set of image points for triangle X’Y’Z’?
X’(1, 1), Y’(-4, 3), Z’(1, 5)
X’(1, 1), Y’(–3, –4), Z’(–1, –5)
X’(–1, 1), Y’(–3, –4), Z’(–5, 1)
X’(–1, –1),Y’(4, –3), Z’(–1, –5)
Answers
Given :- Triangle XYZ has vertices X(1, –1), Y(3, 4), and Z(5, –1). Nikko rotated the triangle 90° counterclockwise about the origin.
To Find :- What is the correct set of image points for triangle X’Y’Z’ ?
A) X’(1, 1), Y’(-4, 3), Z’(1, 5)
B) X’(1, 1), Y’(–3, –4), Z’(–1, –5)
C) X’(–1, 1), Y’(–3, –4), Z’(–5, 1)
D) X’(–1, –1),Y’(4, –3), Z’(–1, –5)
Solution :-
we know that, When we rotate a point 90° counterclockwise about the origin ,
- (x , y) = (-y , x) .
- we have to switch x and y and make y negative .
so,
→ X(1 , -1) = X'{-(-1) , 1} = X'(1 , 1) .
→ Y(3 , 4) = Y'{-(4) , 1} = Y'(-4 , 3) .
→ Z(5 , -1) = Z'{-(-1) , 5} = Z'(1 , 5) .
therefore, the correct set of image points for triangle X’Y’Z’ will be (A) X’(1, 1), Y’(-4, 3), Z’(1, 5) .
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