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

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

Answer Link

MrRoyal MrRoyal · Answer 2 · 2022-05-25T12:10:04+02:00

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

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 :

How to determine the scale factor?

Otras preguntas

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