Respuesta :
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?
Answer:
Scale factor = 1/2
Step-by-step explanation:
Distance formula:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
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
[tex]HJ=\sqrt{(1-(-5))^2+(4-2)^2}\Rightarrow \sqrt{36+4}=\sqrt{40}\Rightarrow 2\sqrt{10}[/tex]
After dilation HJ becomes H'J' with coordinates H'(-1,2) and J'(2,3).
[tex]H'J'=\sqrt{(2-(-1))^2+(3-2)^2}\Rightarrow \sqrt{9+1}=\sqrt{10}[/tex]
Scale factor of dilation is
[tex]\text{Scale factor}=\dfrac{\text{Length of segment of image}}{\text{Length of corresponding segment of preimage}}[/tex]
[tex]\text{Scale factor}=\dfrac{H'J'}{HJ}[/tex]
[tex]\text{Scale factor}=\dfrac{\sqrt{10}}{2\sqrt{10}}[/tex]
[tex]\text{Scale factor}=\dfrac{1}{2}[/tex]
Therefore, the scale factor is 1/2.
