Question

A triangle with vertices at A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertices at A′(0, 0), B′(0, 10), and C′(15, 0). The origin is the center of dilation. What is the scale factor of the dilation? A. 1.5 B. 2 C. 2.5 D. 3

Answer 1

2.5

Explanation:

just got it right

Answer 2

ANSWER

The scale factor is

`2.5`

EXPLANATION

The given triangle has vertices,


`A(0,0),B(0,4),\:and\:C(6, 0)`.

The vertices of the image triangle is,


`A'(0,0),B'(0,10),\:and\:C'(15, 0)`.

The scale factor is given by


`k = (image \: length)/(object \: length)`

So we can use any of the corresponding sides to determine the scale factor,


`k = (|A'B'|)/( |AB|)`


`k = ( |10 - 0| )/( |4 - 0|)`


`k = ( |10| )/( |4 |) = (10)/(4) = 2.5`

Or


`k = (|A'C'|)/( |AC|)`


`k = ( |15 - 0| )/( |6 - 0|)`


`k = ( |15| )/( |6|) = (15)/(6) = 2.5`


Or


`k=(|B'C'|)/(|BC|)`


`k = (√((15 - 0)^2+(0-10)^2 ))/(√((6 - 0)^2+(0-4)^2))`


`k = ( 5√(13))/(2√(13)) = (5)/(2) = 2.5`

The correct answer is C