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A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4). If A' has coordinates of (–0.25, 0.5) after the triangle has been dilated with a center of dilation about the origin, which statements are true? Check all that apply.

The coordinates of C' are (0.75, 0.5).

The coordinates of C' are (1.5, 1).

The scale factor is 1/8.

The scale factor is 8.

The scale factor is 1/4.

The scale factor is 4. The coordinates of B' are (–0.25, 1).

The coordinates of B' are (–0.5, 2).

Respuesta :

General Idea:

When we are given a point P(x, y) centered at origin with a scale factor of k, then the dilated point will be given by P' (kx, ky)

Applying the concept:

Given A(-2, 4) and A'(-0.25, 0.5), which means [tex] x = -2 [/tex], and [tex] kx = -0.25 [/tex].

Substituting -2 for x in the equation [tex] kx = -0.25 [/tex], we get the below equation:

[tex] -2k=-0.25\\ \frac{-2k}{-2} =\frac{-0.25}{-2}\\ k=0.125\\ k=\frac{1}{8} [/tex]

Now we need to find B' and C' by multiplying 0.125 with the x-coordinate and y-coordinate.

-----

x-coordinate of B is -2, y-coordinate of B is 8

x-coordinate of B' [tex] =-2*0.125=-0.25 [/tex]

y-coordinate of B'[tex] =8*0.125=1 [/tex]

So [tex] B' = (-0.25, 1) [/tex]

-----

x-coordinate of C is 6 and y-coordinate of C is 4

x-coordinate of C'[tex] =0.125*6=0.75 [/tex]

y-coordinate of C'[tex] =0.125*4=0.5 [/tex]

So [tex] C' = (0.75, 0.5) [/tex]

Conclusion:

The below are the TRUE statements:

(i) The coordinates of C' are (0.75, 0.5)

(ii) The scale factor is 1/8

(iii) The coordinates of B' are (–0.25, 1).

MrRoyal

Dilations involve changing the size of a triangle

The true options are (a), (c) and (f)

The coordinates of the triangle are given as:

A = (-2, 4),

B = (-2, 8),

C = (6, 4).

The coordinates of the image of the triangle are given as:

A' = (-0.25, 0.5)

Start by calculating the scale factor (k)

[tex]\mathbf{k = \frac{A'}{A}}[/tex]

So, we have:

[tex]\mathbf{k = \frac{(-0.25,0.5)}{(-2,4)}}[/tex]

Divide

[tex]\mathbf{k = \frac 18}[/tex]

This means that option (c) is correct

Next, calculates the coordinates of C' using

[tex]\mathbf{C' = C \times k}[/tex]

So, we have:

[tex]\mathbf{C' = (6,4) \times \frac18}[/tex]

[tex]\mathbf{C' = (0.75,0.5)}[/tex]

This means that option (a) is correct

Next, calculates the coordinates of B' using

[tex]\mathbf{B' = B \times k}[/tex]

So, we have:

[tex]\mathbf{B' = (-2,8) \times \frac18}[/tex]

[tex]\mathbf{B' = (-0.25,1)}[/tex]

This means that option (f) is correct

Hence, the true options are (a), (c) and (f)

Read more about dilations at:

https://brainly.com/question/13176891

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