Question

what sequence of transformations will map a triangle from (1,1), (3,1), and (2,4) to (-1,-1), (-3,-1), and (-2,-4)? a. dilation by 0.5, reflection over the y - axis b. translation 3 units right, reflection over y - axis c. reflection over the y - axis d. rotation 180 degrees which transformation does not preserve the size of a figure?

Explanation:

Step1: Analyze the first question

For a point \((x,y)\) rotated 180 - degrees, the new point is \((-x,-y)\). The points \((1,1)\), \((3,1)\), \((2,4)\) become \((-1,-1)\), \((-3,-1)\), \((-2,-4)\) after 180 - degree rotation. A dilation by 0.5 and reflection over y - axis or translation 3 units right and reflection over y - axis or just reflection over y - axis will not map the triangle in the required way.

Step2: Analyze the second question

Translation, reflection, and rotation are rigid motions that preserve the size and shape of a figure. Dilation changes the size of a figure by a scale factor. So dilation does not preserve the size of a figure.

Answer:

1. D. Rotation 180 degrees
2. Dilation