Question

The coordinates of the vertices of△rst are r(−4, −1), s(−1, −1), and t(−4, −2). the coordinates of the vertices of△r′s′t′ are r′(1, −2), s′(1, 1), and t′(2, −2). drag and drop the answers into the boxes to correctly complete the statement.

The transformation from △RST to △R'S'T' involves a _________.

A) Reflection over the x-axis
B) Reflection over the y-axis
C) Translation upwards
D) Rotation by 90 degrees
E) Translation to the left

Answer 1

The transformation from △RST to △R'S'T' is a translation horizontally to the right by 5 units and vertically downward by 1 unit.

Step-by-step explanation:

The transformation from △RST to △R'S'T' involves translation horizontally to the right side of the coordinate system and vertically downward in the coordinate system. To determine this, we can look at the change in the coordinates from the original triangle to the transformed triangle. For instance, point R at (-4, -1) moves to R' at (1, -2), which is a horizontal shift to the right by 5 units and a vertical shift downwards by 1 unit. The same shift can be observed for the other points, S and T, which are translated to S' and T' respectively. No reflection or rotation has taken place since the orientation of the triangle has not changed and all points have been shifted by the same amount in the same direction. Therefore, the transformation equations x' = x + 5 and y' = y - 1 can describe the movement of the vertices from △RST to △R'S'T'.