Question

Fill in the gaps below:

A. Triangle A is rotated _____ about (-1,0) to give Triangle A'.
Triangle A' is then reflected in the line ______ to give Triangle A''
b. what type of single transformation maps triangle A onto Triangle A''?

Answer 1

• 90° CCW
• y = 0 (x-axis)
• reflection in the line x+y=-1

Explanation:

You want to know the parts of the composition of transformations that will map triangle A to A', then to A''. You also want to know what single transformation accomplishes the same thing.

A. Rotation, Reflection

The long side of triangle A points "south". In triangle A', it points "east". To transform a segment pointing south to one pointing east requires a rotation of +90°, or 90° CCW.

The long side of triangle A' lies along the line y=1. In triangle A'', it lies on the line y=-1. The line of reflection is halfway between these values, at ...

y = (1 +(-1))/2 = 0/2 = 0

The line of reflection is y=0, the x-axis.

B. Single transformation

We know the transformation involves a reflection. The line of reflection can be found by finding the midpoints of the original and final vertices of the triangle.

The midpoint of the largest acute angle's vertex is ...

((2, -3) +(2, -3))/2 = (2, -3)

The midpoint of the right angle vertex is ...

((0, -3) +(2, -1))/2 = (1, -2)

The line through these two points is ...

x +y = -1

The transformation of A to A'' is a reflection in the line x+y=-1.