Question

Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has vertices
X'(–3, 1), Y'(0, 0), and Z'(–2, –1). Which rule describes the transformation?

Answer 1

the rule is (x - 3, y - 3).

Answer 2

Answer:

Rotation about 90° counter clockwise (x , y)  →→ ( -y, x ).

Step-by-step explanation:

Given  : Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has vertices  X'(–3, 1), Y'(0, 0), and Z'(–2, –1).

To find : Which rule describes the transformation.

Solution : We have given

vertices X(1, 3) →→ X'(–3, 1)

Y(0, 0) →→ Y'(0, 0),

Z(–1, 2) →→ Z'(–2, –1).

Here , we can see in each coordinates value of y become -x and x  become y.

(x , y)  →→ ( -y, x ) this the rule of rotation about 90° counter clockwise.

Therefore,  rotation about 90° counter clockwise (x , y)  →→ ( -y, x ).