Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly 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
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.