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′?
A sequence of transformations that maps △RST to △R′S′T′ is a _______followed by a __________.
- reflection across y axis
- translation 1 unit up
- rotation of 180 degress about the orgin
- rotation of 90 degrees counterclockwise about the orgin

Answer 1

To map △RST to △R′S′T′, we need to perform a reflection across the y-axis followed by a translation 1 unit up.

Step-by-step explanation:

To map △RST to △R′S′T′, we need to perform a reflection across the y-axis followed by a translation 1 unit up. This sequence of transformations will change the coordinates of each vertex to their corresponding coordinates in △R′S′T′.

1. Reflection across y-axis: As we reflect a point across the y-axis, the x-coordinate of the point changes sign, while the y-coordinate remains the same. So, the reflection of R(−3, −1) will be R′(3, −1), the reflection of S(−1, −1) will be S′(1, −1), and the reflection of T(−4, −5) will be T′(4, −5).

2. Translation 1 unit up: We need to add 1 to the y-coordinate of each vertex. So, R′(3, −1) becomes R′S′T′(3, 0), S′(1, −1) becomes S′′(1, 0), and T′(4, −5) becomes T′′(4, −4).