<h2>
Answer with explanation:</h2>
- Translation is a rigid motion that is used in geometry to trace a function that moves points of a figure a particular distance.
- A reflection is also a rigid motion that produces a reflection image of a particular figure across a line of reflection.
- Dilation enlarges of reduce a figure by using a scale factor.
Given : Δ XYZ, with vertices X(-2, 0), Y(-2, -1), and Z(-5, -2), undergoes a transformation to form Δ X′Y′Z′, with vertices X′(4, -2), Y′(4, -3), and Z′(1, -4).
We can see that the x-coordinate of X (-2) moves 6 units to the right (i.e. -2+6) to get x-coordinate of X'(4).
[∵ -2+6=4]
Similarly, x-coordinates of Y (-2) and Z'(1) moves 6 units to the right to get x-coordinate of Y'(4) and Z'(1) respectively.
Also, the y-coordinate of X (0) moves 2 units to the down to get y-coordinate of X'(-2).
[∵ 0-2=-2]
Similarly, y-coordinates of Y (-1) and Z'(-2) moves 2 units to the down to get x-coordinate of Y'(-3) and Z'(-4) respectively.
Therefore, Δ XYZ undergoes a <u>translation of 6 units right and 2 units down</u>.
Also, it is given that :- Δ X′Y′Z′ then undergoes a transformation to form Δ X′Y′Z′, with vertices X″(4, 2), Y″(4, 3), and Z″(1, 4).
We note that the x-coordinate of each corresponding points remains sam but the sign of y-coordinate changed.
It happens if the figure undergoes under reflection across the x-axis.
Therefore, Δ X′Y′Z′ undergoes a <u>reflection across the x-axis</u>.
