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Rectangle ABCD with coordinates A(1, 1), B(4, 1), C(4, 2), and D(1, 2) dilates with respect to the origin to give rectangle A'B'C'D'. If A'B' = 6, what is the scale factor of the dilation?
a) 6
b) 3
c) 2
d) 1/2
e) 4

Respuesta :

HomertheGenius
First we have to find the length of AB:
AB² = ( 1 - 1 )² + ( 4 - 1 )²
AB² = 0² + 3²
AB² = 9
AB = √9 = 3
A`B` = 6
A`B` = k * 3
6 = k * 3
k = 2
Answer:
The scale factor of the dilation is
C ) 2
MrRoyal

The scale factor of the dilation of the rectangle ABCD is 2

How to determine the scale factor?

The coordinates are given as:

A(1, 1), B(4, 1), C(4, 2)

The points A and B have the same y-coordinate.

So, the distance AB is:

AB = 4 - 1

Evaluate

AB = 3

The scale factor (k) is then calculated using:

k = A'B'/AB

This gives

k = 6/3

Evaluate

k = 2

Hence, the scale factor of the dilation is 2

Read more about dilation at:

https://brainly.com/question/3457976

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