Atriangle with vertices (2, 9), (5, 1), and (1, 4) is dilated by a scale factor of 4. which matrix expression represents the transformation?

The matrix expression that represents the transformation is:

         Option: C

We are given a vertices of a triangle as:

                           (2, 9), (-5, 1), and (1,- 4)

This means that in the matrix representation these vertices could be represented as:

Now, when these vertices are dilated by a scale factor of 4, the change in vertices are:

Each of the vertices are multiplied by 4.

i.e. each of the entry in the matrix is multiplied by 4.

or we can take common 4 from the matrix to obtain the transformed vertices in the form as:

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)