Question

The coordinates of the vertices of △RST are R(−3, −1) , S(−1, −1) , and T(−4, −5) . The coordinates of the vertices of △R′S′T′ are R′(1, −2) , S′(1, 0) , and T′(5, −3) . What is the sequence of transformations that maps △RST to △R′S′T′? Drag and drop the answers into the boxes to correctly complete the statement.
A sequence of transformations that maps △RST to △R′S′T′ is a______ followed by a ______.

Translation 1 unite up

Rotation 180* about the orgin

Reflection across the y-axis

Rotation of 90* counterclockwise about the origin

(Pick two in order of the sentence.)

Answer 1

You are given triangle RST with vertices R(-3,-1), S(-1,-1) and T(-4,-5).

1. Apply the rotation of 90° counterclockwise about the origin that has a rule:

(x,y)→(-y,x).

Then

• R(-3,-1)→R''(1,-3),
• S(-1,-1)→S''(1,-1),
• T(-4,-5)→T''(5,-4).

2. Second transformation is translation 1 unite up with a rule:

(x,y)→(x,y+1).

So

• R''(1,-3)→R'(1,-2);
• S''(1,-1)→S'(1,0);
• T''(5,-4)→T'(5,-3).

As you can see these points are exactly those from the task condition.

Answer: 1st transfomation is rotation of 90° counterclockwise about the origin and 2nd transformation is translation 1 unite up