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rewona [7]
3 years ago
12

The line represented by 2y = x + 8 is dilated by a scale factor of k centered at the origin, such that the image of the line has

an equation of y - 12x = 2. What is the scale factor?
Mathematics
1 answer:
Mandarinka [93]3 years ago
4 0

Answer:

k=\frac{1}{2}

Step-by-step explanation:

we know that

A dilation is a non rigid transformation that produce similar figures

If two lines are similar, then the lines are parallel

Lines parallel have the same slope

so

we have

Line A

2y=x+8

isolate the variable y

y=0.5x+4 ----> equation A

The slope of the line A is m=0.5

The y-intercept of the line A is b=4

Line B

y-\frac{1}{2}x=2

isolate the variable y

y=\frac{1}{2}x+2 ----> equation B

The slope of the line B is m=0.5

The y-intercept of the line B is b=2

Remember that

The y-intercept of line A multiplied by the scale factor k must be equal to the y-intercept of line B

so

4k=2

solve for k

k=\frac{1}{2}

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