Answer:
The length of A'B' is 15 units
Step-by-step explanation:
As line segment AB has end points
The distance formula to calculate the distance between two points is given by:
[tex]{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}}[/tex]
[tex]{\displaystyle d={\sqrt {(20-4)^{2}+(4-16)^{2}}}}[/tex]
[tex]d=\sqrt{16^2+(-12)^2}[/tex]
[tex]d=\sqrt{256+144}[/tex]
[tex]d=\sqrt{400}[/tex]
[tex]d=20[/tex]
[tex]d=20[/tex] is also the length of the line segment AB.
As segment will be dilated with a scale factor of 3/4 and a center at the origin to create A'B'.
So,
The length of A'B' can be obtained by multiplying the length of AB by 3/4
Therefore,
The length of A'B' = 3/4 × 20 = 15
So, the length of A'B' is 15 units.
Keywords: dilation, distance formula, length, line segment
Learn more about dilation from brainly.com/question/10185868
#learnwithBrainly
