Question

If line q bisects EG at point T, and if ET= 1/3 x and TG= x-2, then find EG

please help I have no idea how to do this its geometry problem for my math hw even my parents and siblings who are older than me don't know how to do this

Answer 1

EG =
`(4x)/(3) - 2`

Explanation:

( First check the attached image for diagram )

`EG=ET+TG`

Substituting the given values,

`EG = (1)/(3)x + (x - 2)`

Opening the brackets and multiplying,

`EG = (1 * x)/(3) + x - 2`

`= > EG = (x)/(3) + x - 2`

Finding LCM,

`= > EG = ( (x)/(3) + (x * 3)/(1 * 3) ) - 2`

`= > EG = ( (x)/(3) + (3x)/(3)) - 2`

Combining them,

`EG =( (x + 3x)/(3)) - 2`

`EG = (4x)/(3) - 2`

Note:- T is midpoint of EG

because ET = TG

Answer 2

EG = 2 units

Explanation:

Given that line q bisects EG at T , then

ET = TG ( substitute values )

`(1)/(3)` x = x - 2 ( multiply through by 3 to clear the fraction )

x = 3x - 6 ( subtract x from both sides )

0 = 2x - 6 ( add 6 to both sides )

6 = 2x ( divide both sides by 2 )

3 = x

Then

ET =
`(1)/(3)` x =
`(1)/(3)` × 3 = 1

TG = x - 2 = 3 - 2 = 1

Thus

EG = ET + TG = 1 + 1 = 2 units