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The composition do,0.75(x,y) ∘ do,2(x,y) is applied to △lmn to create △l''m''n''. which statements must be true regarding the two triangles? check all that apply. ∠m ≅ ∠m'' △lmn ~ △l''m''n'' △lmn ≅ △l''m''n'' the coordinates of vertex l'' are (-3, 1.5). the coordinates of vertex n'' are (3, -1.5). the coordinates of vertex m'' are (1.5, -1.5).

Respuesta :

ilikea

Answer:

A.  ∠M ≅ ∠M''

B.  △LMN ~ △L''M''N''

E.  The coordinates of vertex N'' are (3, -1.5).

Step-by-step explanation:

MrRoyal

Transformation involves changing the position and size of a shape.

The true statements are:

  • [tex]\mathbf{\angle m \cong \angle m"}[/tex].
  • [tex]\mathbf{\triangle lmn \sim \triangle l"m"n"}[/tex].
  • The coordinates of n" are [tex]\mathbf{N" = (3,-1.5)}[/tex].

The coordinates of the triangle are:

[tex]\mathbf{L = (-1, 2)}[/tex]

[tex]\mathbf{ M = (-1, -1)}[/tex]

[tex]\mathbf{N = (2, -1)}[/tex]

The transformation rule is given as:

[tex]\mathbf{do, 0.75(x,y)\circ,2(x,y)}[/tex]

The transformation rule is a dilation by a factor of 0.75, and then a factor of 2.

Uniform dilation changes the size of a shape, but the angles remain unchanged. This means that:

  • [tex]\mathbf{\angle l \cong \angle l"}[/tex].
  • [tex]\mathbf{\angle m \cong \angle m"}[/tex].
  • [tex]\mathbf{\angle n \cong \angle n"}[/tex].
  • [tex]\mathbf{\triangle lmn \sim \triangle l"m"n"}[/tex]

The above highlights means that:

  • The angles of both triangles are congruent
  • The triangles are similar

Next, we apply the rule on the coordinates of the triangle

[tex]\mathbf{L" = 0.75 \times 2 \times (-1,2)}[/tex]

[tex]\mathbf{L" = (-1.5,3)}[/tex]

[tex]\mathbf{M" = 0.75 \times 2 \times (-1,-1)}[/tex]

[tex]\mathbf{M" = (-1.5,-1.5)}[/tex]

[tex]\mathbf{N" = 0.75 \times 2 \times (2,-1)}[/tex]

[tex]\mathbf{N" = (3,-1.5)}[/tex]

Hence, the true statements are:

  • [tex]\mathbf{\angle m \cong \angle m"}[/tex].
  • [tex]\mathbf{\triangle lmn \sim \triangle l"m"n"}[/tex].
  • The coordinates of n" are [tex]\mathbf{N" = (3,-1.5)}[/tex].

Read more about transformations at:

https://brainly.com/question/11709244

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