A triangle with vertices at A(20, –30), B(10, –15), and C(5, –20) has been dilated with a center of dilation at the origin. The image of B, point B prime, has the coordinates (2, –3). What is the scale factor of the dilation? StartFraction 1 Over 10 EndFraction One-fifth 5 10

One-fifth

Step-by-step explanation:

step 1

Find the distance between the origin and the point B

the formula to calculate the distance between two points is equal to

we have

O (0,0) and B(10, –15)

substitute

step 2

Find the distance between the origin and the point B'

the formula to calculate the distance between two points is equal to

we have

O (0,0) and B'(2,-3)

substitute

step 3

Find the scale factor of the dilation

The scale factor is equal to divide the length of segment OB' by the length of segment OB

so

so

One-fifth

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x