A line segment has endpoints at (9 ,1 ) and (1 ,2 ). The line segment is dilated by a factor of 4 around (3 ,3 ). What are the new endpoints and length of the line segment?

1 Answer
Leland Adriano Alejandro
Jun 23, 2016

The new endpoints are A'(x_a', y_a')=(27, -5) and B'(x_b', y_b')=(-5, -1)

Explanation:

Let A(x_a, y_a)=(9, 1) and B(x_b, y_b)=(1, 2)

Dilated by a factor of 4

Let A'(x_a', y_a') and
Let B'(x_b', y_b') be the new points

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Let us solve the new point A'(x_a', y_a')

Working equation to solve x_a'

(x_a'-3)/(x_a-3)=4/1

(x_a'-3)/(9-3)=4/1

(x_a'-3)/6=4

x_a'=27

Working equation to solve y_a'

(y_a'-3)/(y_a-3)=4/1

(y_a'-3)/(1-3)=4/1

(y_a'-3)/(-2)=4

y_a'=-5

the new point A'(x_a', y_a')=(27, -5)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let us solve the new point B'(x_b', y_b')

Working equation to solve x_b'

(x_b'-3)/(x_b-3)=4/1

(x_b'-3)/(1-3)=4/1

(x_b'-3)/-2=4

x_b'=-5

Working equation to solve y_b'

(y_b'-3)/(y_b-3)=4/1

(y_b'-3)/(2-3)=4/1

(y_b'-3)/(-1)=4

y_b'=-1

the new point B'(x_b', y_b')=(-5, -1)

Kindly see the graph of the segments
Desmos

God bless....I hope the explanation is useful.

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