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sergejj [24]
3 years ago
12

Line segment QR is dilated to create line segment Q'R'

Mathematics
2 answers:
leva [86]3 years ago
8 0

Answer:

3 Units on edge

Step-by-step explanation:

Lelechka [254]3 years ago
4 0

Answer:

The distance between R and R' is 3 units ⇒ 1st answer

Step-by-step explanation:

<u><em>A dilation</em></u> is a transformation that produces an image that is the same

shape as the original, but in a different size.

If the image is larger than the original figure then dilation is called an

enlargement.

If the image is smaller than the original figure then the dilation

is called a reduction.

The image of a line by dilation parallel to the original line if the original

line not passes through the center of dilation.

<em>Line segment QR is dilated to create line segment Q'R'</em>

∴ QR is parallel to Q'R'

<em>The factor of dilation is 1.5</em>

∴ The length of Q'R' is 1.5 the length of QR

In Δs TRQ and TR'Q'

∵ QR // Q'R'

∴ m∠TRQ = m∠TR'Q'

∴ m∠TQR = m∠TQ'R'

∵ ∠T is common in the two triangles

∴ ΔTRQ is similar to ΔTR'Q'

∴ \frac{TR'}{TR}=\frac{R'Q'}{RQ}

∵ \frac{Q'R'}{QR}=1.5

∵ TR' = TR + y

∵ Tr = 6 units

∴ TR' = 6 + y units

∵ \frac{TR'}{TR}=\frac{6+y}{6}

∴ 1.5=\frac{6+y}{6}

Multiply both sides by 6

∴ 9 = 6 + y

Subtract 6 from both sides

∴ 3 = y

* The distance between R and R' is 3 units

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