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guapka [62]
3 years ago
6

A rectangle on the coordinate plane has vertices at (0,0), (3,0), (3,2), and (0,2). A dialation of the rectangle has vertices at

(0,0), (9,0), (9,6), and (0,1). Find the scale factor
Mathematics
1 answer:
professor190 [17]3 years ago
4 0

Answer: The scale factor is 3.

Step-by-step explanation:

1. You kwnow that original rectangle has the following coordinates in its vertices:

 (0,0), (3,0), (3,2), and (0,2)

2. After dilation, the rectangle has vertices at (0,0), (9,0), (9,6), and (0,1). Therefore, you can calculate the scale factor as following:

Let's call k the scale factor and let's choose one the coordinates of the original rectangle and the same coordinate after dilation:

Original vertex: (3,2) ; Vertex after dilation: (9,6)

Then:

3k=9

k=3

2k=6

k=3

The scale factor is 3.

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Given

x^5*k=a .................(1)

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We need to find x^3.

Solution:

On inspection, we note that (1)/(2) gives x^3 on the left hand side, but the division is valid on conditions that x &ne; 0 and k &ne; 0.

So we conclude:

(1) / (2)

\frac{x^5*k}{x^2*k^2} = \frac{a}{b}

=>

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=>

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