Question

(please help madal given to best answer)
1. A segment with endpoints (2,-1) and (4,2) is dilated to the image segment with endpoints (4,-2) and (8,4). What is the scale factor for the dilation.
A. 2
B. 4
C. 6
D. 8
2. The side lengths of two different cubes are 35cm and 42cm. What is the ratio of the volume of the smaller to the volume of the larger (in simplest form)?
A. 175/240
B. 125/216
C. 25/36
D. 5/6

Answer 1

@mathstudent55

Answer 2

Problem 1.
Compare the endpoints (2, -1) and (4, -2). This is a dilation, so we need to multiply or divide.

What do you do to the numbers 2 and -1 to end up with 4 and -2, respectively?

Now compare the other two endpoints. What do you do to the numbers 4 and -2 to end up with 4 and -8? [BTW, you have the last point as (4, 8), but I think you meant (4 -8)]

Answer 3

Problem 2.
If you have two solids, like two cubes in this problem, and the ratios of the sides is a:b or a/b, then the ratio of the volumes is a^3:b^3 or a^3/b^3.
In this case, you have two cubes. The ratio of the lengths of the sides is
35/42. The ratio of the volumes is the cube of that fraction.
You need to raise 35/42 to the 3rd power and simplify the fraction.

Answer 4

So for problem 1 the answer is 2 right but I did not get problem 2

Answer 5

and for problem 2 is 125/216 right

Answer 6

You are correct with problem 1.

Problem 2: \( \left( \dfrac{35}{42} \right) ^3\)

Reduce the fraction before cubing it:

\( \left( \dfrac{35}{42} \right) ^3 = \left( \dfrac{7 \times 5}{7 \times 6} \right) ^3
=\left( \dfrac{5}{6} \right) ^3 = \dfrac{5^3}{6^3} = \dfrac{125}{216}\)

You are correct with problem 2 also.