Question

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? x = 2. 25 units x = 2. 5 units x = 4. 25 units x = 4. 5 units.

Answer 1

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

Given that

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 ST is dilated to create line segment S prime T prime.

The length of QT is 1. 2 and the length of QS is 2.

The length of SS prime is x and the length of TT prime is 1. 5.

We have to determine

What is x, the distance between points S' and S?

According to the question

Line segment ST is dilated to create line segment S'T' using the dilation rule DQ, 2.25.

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

Since the line ST is dilated to S'T' with the center of dilation Q, 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.

$\dfrac{SQ}{S'Q} = \dfrac{TQ}{T'Q}\\ \\ \dfrac{SQ}{SQ+SS} = \dfrac{TQ}{TQ+TT'}\\ \\ \dfrac{2}{2+x} = \dfrac{1.2}{1.2+1.5}\\\rm \\ \dfrac{2}{2+x} = \dfrac{1.2}{2.7}\\\\ \dfrac{2}{2+x} = \dfrac{12}{27}\\\\2(27) = (2+x) 12\\\\ 54 = 24 + 12x\\ \\ 12x = 54-24\\ \\ 12x=30\\ \\ x = \dfrac{30}{12}\\ \\ x = 2.5$

Hence, the distance between points S' and S is x= 2.5 units.

To know more about Pythagoras Theorem click the link given below.

brainly.com/question/16016926