Question

:Select the correct answer from each drop-down menu.

Answer 1

Answer:

Translation

Reflection about x- axis

Step-by-step explanation:

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

$(x,y)\rightarrow (x+6,y-2)$

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

$(x,y)\rightarrow (x,-y)$

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

Answer 2

Once again, Brainly chokes on my answer, so you get it as a picture.

1) translation

2) reflection