Question

Line WY is dilated to create line W'Y' using point Q as
the center of dilation.
What is the scale factor?
Given that QY' = 4.125, what is QY?
(Can someone show me how to get the scale factor please with the answer?)

Answer 1

Answer:

What is the scale factor?  

2.75

 

Given that QY' = 4.125, what is QY?  

1.5

Step-by- step

Edge 2020

Answer 2

The length of the line segment QY is 1.5 units.

The scale factor due to dilation is 2.75.

The lines WY and W'Y' are parallel and there is QY'W' as a triangle.

Thus we can use property of parallel line intersecting a triangle:

$\dfrac{QY}{QY'} = \dfrac{QW}{QW'}\\= QY = 4.125 \times \dfrac{2}{5.5}\\= 1.5$

Now draw a line parallel to QY' passing through point W as shown in below diagram.

Now again using same proportionate sectioning by parallel line in triangle property:

$\dfrac{PY'}{W'Y'} = \dfrac{WQ}{W'Q}\\\dfrac{PY'}{W'Y'} =\dfrac{2}{5.5}\\\\W'Y' = PY' \times \dfrac{5.5}{2}$

Since WPY'Y is a parallelogram, thus we have length of WY = length of PY'.

Or we thus have:

$W'Y' = \dfrac{5.5}{2}\times WY\\= 2.75 WY$

Thus W'Y' is 2.75 times scaled as compared to WY. This is the needed scale factor and above is the method how you calculate it for such situations.

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