Atriangle 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).

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 , and .

Substituting -2 for x in the equation , we get the below equation:

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

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

x-coordinate of B'

y-coordinate of B'

So

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

x-coordinate of C'

y-coordinate of C'

So

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).

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)

So, we have:

Divide

This means that option (c) is correct

Next, calculates the coordinates of C' using

So, we have:

This means that option (a) is correct

Next, calculates the coordinates of B' using

So, we have:

This means that option (f) is correct

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

Read more about dilations at:

link

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.