Mathematics: Suppose hj is on s coordinate plane located at h(-5,2) and j(1,4). under a dilation centered at(3,2), hj becomes h j with coordinates h (-1,2) and j (2,3). what is the scale factor for this dilation?

maybe this can help wait is it a time quizStep-by-step explanation:...

Suppose hj is on s coordinate plane located at h(-5,2)

ineedhelpplz40

12.03.2022

Scale factor = 1/2

Step-by-step explanation:

Distance formula:

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

It is given that on a coordinate plane two points are located at H(-5,2) and J(1,4).

Using distance formula we get

$HJ=\sqrt{(1-(-5))^2+(4-2)^2}\Rightarrow \sqrt{36+4}=\sqrt{40}\Rightarrow 2\sqrt{10}$

After dilation HJ becomes H'J' with coordinates H'(-1,2) and J'(2,3).

$H'J'=\sqrt{(2-(-1))^2+(3-2)^2}\Rightarrow \sqrt{9+1}=\sqrt{10}$

Scale factor of dilation is

$\text{Scale factor}=\dfrac{\text{Length of segment of image}}{\text{Length of corresponding segment of preimage}}$

$\text{Scale factor}=\dfrac{H'J'}{HJ}$

$\text{Scale factor}=\dfrac{\sqrt{10}}{2\sqrt{10}}$

$\text{Scale factor}=\dfrac{1}{2}$

Therefore, the scale factor is 1/2.

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