MATH SOLVE

2 months ago

Q:
# Given: line segment AB is 10 inches long. Find the length of A'B' if AB is dilated to form A'B' with a scale factor of 1 2 . A) 1 2 inches B) 5 inches C) 10 inches D) 20 inches

Accepted Solution

A:

ANSWER

[tex]|A'B'| = 5 \: units[/tex]

EXPLANATION

The formula for calculating the scale factor is

[tex]k = \frac{image \: length}{object \: length} [/tex]

Or

[tex]k = \frac{ |A'B'| }{ |AB|} [/tex]

Where k is the scale factor.

We were given

[tex] |A'B'|=10[/tex]

This is the image length.

We substitute the scale factor and the image length in to the formula to get,

[tex] \frac{1}{2} = \frac{ |A'B'| }{ 10} [/tex]

Multiply both sides by 10 to get,

[tex] \frac{1}{2}\times 10= |A'B'|[/tex]

[tex]|A'B'| = 5 \: units[/tex]

[tex]|A'B'| = 5 \: units[/tex]

EXPLANATION

The formula for calculating the scale factor is

[tex]k = \frac{image \: length}{object \: length} [/tex]

Or

[tex]k = \frac{ |A'B'| }{ |AB|} [/tex]

Where k is the scale factor.

We were given

[tex] |A'B'|=10[/tex]

This is the image length.

We substitute the scale factor and the image length in to the formula to get,

[tex] \frac{1}{2} = \frac{ |A'B'| }{ 10} [/tex]

Multiply both sides by 10 to get,

[tex] \frac{1}{2}\times 10= |A'B'|[/tex]

[tex]|A'B'| = 5 \: units[/tex]