Question

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

Answer 1

Answer: x = 2.5 units

Explanation:

Given : Line segment ST is dilated to create line segment S'T' using the dilation rule
`D_(Q, 2.25)`.

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

We know that , dilation creates similar figures.

If we consider the given situation, we get

⇒ ΔSTQ and ΔS'T'Q must be similar.

Corresponding sides of similar triangle must be proportional .

`\Rightarrow\ (TQ)/(TT')=(SQ)/(SS')\\\\\Rightarrow(1.2)/(1.5)=(2)/(x)\\\\\Rightarrow\ x=(2)/(1.2)*1.5\\\\\Rightarrow\ x=2.5`

Hence, the distance between points S and S = 2.5 units

Answer 2

SS' = 2.5

Explanation:

The distances on segment QS' are 2/1.2 = 5/3 times those of corresponding parts on segment QT'.

5/3 · 1.5 = 2.5