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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 _____

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 . _

We are given that a triangle XYZ with verticesX(-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).

X=(-2,0) and X'=(4,-2)

x=-2,x'=4

x'-x=4-(-2)=6

y=0,y'=-2

y'-y=-2-0=-2

Y(-2,-1) and Y'(4,-3)

x'-x=4+2=6

y'-y=-3+1=-2

Z(-5,-2) and Z'(1,-4)

x'-x=1+5=6

y'-y=-4+2=-2

The vertices of triangle XYZ change into vertices of triangle X'Y'Z' by the rule

[tex](x,y)\rightarrow (x+6,y-2)[/tex]

Hence, the type of transformation that triangle XYZ undergoes is a translation.

Triangle X'Y'Z' undergoes a transformation to form triangle X''Y''Z'' with vertices X''(4,2),Y''(4,3) and Z''(1,4).

We can see that y- coordinate of every point of triangle X'Y'Z' change into positive and x - coordinate remain same.

Reflection about x- axis

[tex](x,y)\rightarrow (x,-y)[/tex]

Hence, the type of transformation that triangle X'Y'Z' undergoes is a reflection about x- axis.