Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Line segment st is dilated to create line segment s't' using the dilation rule dq,2.25. point q is the center of dilation. line segment s t is dilated to create line segment s prime t prime. the length of q t is 1.2 and the length of q s is 2. the length of s s prime is x and the length of t t prime is 1.5. what is x, the distance between points s' and s?

Sagot :

The distance between points S' and S is 2.5 units.

What is proportionality theorem in triangles?

If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

Given that,

line segment ST is dilated to create line segment S'T' using the dilation rule DQ.

Also, SQ = 2 units, TQ = 1.2 units, TT'=1.5 units, SS' = x units.

We need to find the value of x, the distance between points S' and S.

Since the line ST is dilated to S'T' with center of dilation Q, so the triangles STQ and S'T'Q must be similar.

We know that the corresponding sides of two similar triangles are proportional.

So, from ΔSTQ and ΔS'T'Q, we get

[tex]\frac{SQ}{S'Q} =\frac{TQ}{T'Q}[/tex]

[tex]\frac{SQ}{SQ+S'S} =\frac{TQ}{TQ+T'Q}[/tex]

[tex]\frac{2}{2+x} =\frac{1.2}{1.2+1.5}[/tex]

[tex]\frac{2}{2+x} =\frac{1.2}{2.7}[/tex]

[tex]\frac{2}{2+x} =\frac{12}{27}[/tex]

[tex]\frac{1}{2+x} =\frac{6}{27}[/tex]

12+6x = 27

6x = 15

x = 2.5

Hence, Thus, the required value of x is 2.5 units.

To learn more about proportionality theorem from the given link:

https://brainly.com/question/2475257

#SPJ4

View image tutorconsortium345
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.