Question

figure stuv is the result of a transformation on figure opqr. which transformation would accomplish this?
answer
a translation 4 units left and 1 unit down
a translation 1 unit right and 4 units up
a reflection over the x -axis
a reflection over the y -axis

Explanation:

Step1: Analyze key points

First, identify corresponding points of the two figures. For example, take point \( Q \) in \( OPQR \) and its corresponding point \( U \) in \( STUV \). The coordinates of \( Q \) are \( (3, 0) \), and the coordinates of \( U \) are \( (-1, -1) \).

Step2: Calculate translation

To find the horizontal (x - direction) change: \( -1 - 3=-4 \), which means 4 units left. For the vertical (y - direction) change: \( -1 - 0=-1 \), which means 1 unit down. So the transformation is a translation 4 units left and 1 unit down. Also, check reflection: reflection over x - axis would change the sign of y - coordinate, but here the change is not just sign change. Reflection over y - axis would change the sign of x - coordinate, but the change in x is - 4 (not just sign change of 3 to - 3). The other translation option (1 unit right and 4 units up) is opposite to the calculated change.

Answer:

A. translation 4 units left and 1 unit down