Triangle xyz, with vertices x(-2, 0), y(-2, -1), and z(-5, -2), undergoes a transformation to form triangle x′y′z′, with vertices x′(4, -2), y′(4, -3), and z′(1, -4). the type of transformation that triangle xyz undergoes is a

translation 2 units left and 6 units up
reflection across the x-axis
reflection across the y-axis
translation 6 units right and 2 units down
dilation by a scale factor of 2

triangle x′y′z′ then undergoes a transformation to form triangle x′y′z′, with vertices x″(4, 2), y″(4, 3), and z″(1, 4). the type of transformation that triangle x′y′z′ undergoes is a

translation 4 units up
reflection across the x-axis
reflection across the y-axis
translation 6 units right and 2 units down
dilation by scale factor of 2

Answer with explanation: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 translation of 6 units right and 2 units down.

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 reflection across the x-axis.

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