Question

Triangle RST has vertices R(6, 5), S(9, −4), and T(10, 1). Triangle RST has vertices R′(6, −5), S′(9, 4), and T′(10, −1).

Which transformation of triangle RST produced triangle RST?


1.a rotation of 90° clockwise around the origin

2.a rotation of 90° counterclockwise around the origin

3.a reflection across the y-axis

4.a reflection across the x-axis

Answer 1

The transformation that produced triangle R'S'T' is a reflection across the x-axis.

Step-by-step explanation:

In order to determine the transformation that produced triangle R'S'T' (R' is the image of R, S' is the image of S, and T' is the image of T), we can compare the coordinates of the vertices of triangle RST to the coordinates of the vertices of triangle R'S'T'.

If the x-coordinates of the vertices are the same and the y-coordinates have opposite signs, then the transformation is a reflection across the x-axis. If the y-coordinates of the vertices are the same and the x-coordinates have opposite signs, then the transformation is a reflection across the y-axis. If both the x-coordinates and y-coordinates have opposite signs, then the transformation is a rotation of 180° around the origin.

In this case, the x-coordinates of the vertices are the same and the y-coordinates have opposite signs. Therefore, the transformation that produced triangle R'S'T' is a reflection across the x-axis.