Point Q is the center of dilation. Lines segment S U is dilated to form line segment S prime U prime. The length of Q S is 3 .2 and the length of Q U is 4. The length of S S prime is 4.8 and the length of U U prime is x.

Line segment SU is dilated to create S'U' using the dilation rule DQ,2.5.


What is the distance, x, between points U' and U?




4 units

4.8 units

6 units

10 units

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Answer:

Option C.

Step-by-step explanation:

It is given that the dilation rule is [tex]D_{Q,2.5}[/tex]. It means the center of dilatation is point Q and scale factor is 2.5.

Scale factor is the ratio of distance from center to the image of a point and distance from center to the corresponding point.

[tex]\text{Scale factor}=\dfrac{QU'}{QU}[/tex]

It is given that QU=4 and scale factor = 2.5.

[tex]2.5=\dfrac{QU'}{4}[/tex]

Multiply both sides by 4.

[tex]2.5\times 4=QU'[/tex]

[tex]10=QU'[/tex]

We know that

[tex]UU'=QU'-QU[/tex]

[tex]UU'=10-4[/tex]

[tex]UU'=6[/tex]

The distance between U' and U is 6 units.

Therefore, the correct option is C.

Answer:

the answer is c

Step-by-step explanation:

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