contestada

Brian draws a triangle on the coordinate plane and names it AMNB. The dilation
transformation D2 (2,y) = (2x, 2y) is applied to create AM'N'B' = = D2(AMNB)
A third triangle is created from the original triangle with a translation transformation,
AM"NB" =
T<0,10> (AMNB).
Based on the three triangles drawn, which statements are true? Select all that apply.
All three triangles are similar to one another.
Triangle MNB and AM'N'B' are similar to each other, but not to AM"NB".
Triangle MNB and AM"N"B" are similar to each other, but not to AM'N'B'.
None of the triangles are similar to each other.
All three triangles are congruent to one another
Triangle MNB and AM'N'B' are congruent to each other, but not to AM"NB"
Triangle MNB and AM"N"B" are congruent to each other, but not to AM'N'B'
None of the triangles are congruent to each other

Respuesta :

The dilation transformation is a non-rigid transformation while the translation transformation is a rigid transformation.

The true statements are;

  • All three triangles are similar to one another.
  • Triangle ΔMNB and ΔM''N''B'' are congruent to each other but not to ΔM'N'B'.

Reasons:

The given information are;

The transformation applied to ΔMNB to give ΔM'N'B' = A dilation transformation

  • Therefore, ΔM'N'B' = [tex]D_2[/tex](ΔMNB)

The third triangle, ΔM''N''B'', is obtained from the original triangle by a translation transformation as follows;

  • ΔM''N''B'' = [tex]T_{<0, \ 10>}[/tex](ΔMNB)

We have that the sides of the triangle ΔM'N'B' are proportional to the sides

of the triangle ΔMNB by the scale factor of dilation, therefore;

ΔM'N'B' is similar to ΔMNB

A translation transformation is a rigid transformation, therefore;

The dimensions of ΔMNB = The dimensions of ΔM''N''B''

Which gives;

ΔMNB ≅ ΔM''N''B''

Therefore, the true statements are

  • All three triangles are similar to one another.
  • Triangle ΔMNB and ΔM''N''B'' are congruent to each other but not to ΔM'N'B'.

Learn more about the dilation and translation transformation here:

https://brainly.com/question/2644832

https://brainly.com/question/6314707

Otras preguntas