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Galina-37 [17]
3 years ago
7

Segment Y prime Z prime has endpoints located at Y'(0, 3) and Z'(−6, 3). segment YZ was dilated at a scale factor of 3 from the

origin. Which statement describes the pre-image?
A. segment YZ is located at Y (0, 9) and Z (−18, 9) and is three times the size of segment Y prime Z prime.
B. segment YZ is located at Y (0, 3) and Z (−6, 3) and is the same size as segment Y prime Z prime.
C. segment YZ is located at Y (0, 1.5) and Z (−3, 1.5) and is the one-half the size of segment Y prime Z prime.
D. segment YZ is located at Y (0, 1) and Z (−2, 1) and is one-third the size of segment Y prime Z prime.

Mathematics
1 answer:
Klio2033 [76]3 years ago
5 0

Answer:

D. Segment YZ is located at Y(0,1) and Z(−2,1) and is one-third the size of segment Y'Z'

Step-by-step explanation:

When you dilate a point by a factor of x from the origin, you multiply its coordinates by the same factor.

Thus, if the coordinates of the original point are (1,2) and the scale factor is 3, those of its image are (3,6).

If Y'Z' has endpoints at Y'(0,3) and Z'(-6,3) and was dilated by a factor of 3, the coordinates of the endpoints of the pre-image were ⅓ those of the image.

The figure below shows the segments YZ and Y'Z'.

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the ratio of the sides of a certain triangle is 2:7:8 if the longest side of the triangle is 40cm how long are the other two sid
Zigmanuir [339]

The length of the other two sides is 10 and 35 respectively.

<h3>What is a ratio?</h3>

A ratio is a quantitative relation showing the comparison between two or more numbers. It can also be written in the fractional form where the first part is the numerator and the second part is called the denominator.

From the given information:

  • The sides of the triangle = 2:7:8
  • The total sides of the triangle = 2+7+8 = 17

We are being told that the longest side is the triangle is equal to 40.

i.e.

\mathbf{\to\dfrac{8}{17}\times x = 40}

\mathbf{x = 40 \div \dfrac{8}{17}}

\mathbf{x = 40 \times \dfrac{17}{8}}

x = 85

Now for the other two sides 2 and 7, their length is as follows.

\mathbf{\dfrac{2}{17}\times 85 = 10}

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Therefore, we can conclude that the length of the other two sides is 10 and 35 respectively.

Learn more about ratios here:

brainly.com/question/2328454

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