Question

Point T is on line segment \overline{SU} SU . Given TU=x-1,TU=x−1, SU=3x-7,SU=3x−7, and ST=x+7,ST=x+7, determine the numerical length of \overline{TU}. TU .

Answer 1

TU = 12 units

Explanation:

Given that T is a point on line segment SU.

So that;

SU = ST + TU

But, SU = 3x - 7, TU = x - 1, and ST = x + 7.Thus,

SU = ST + TU

3x - 7 = (x + 7) + (x - 1)

3x - 7 = x + 7 + x - 1

3x - 7 = 2x + 6

Collecting like terms.

3x - 2x = 6 + 7

x = 13

Therefore,

TU = x - 1

= 13 - 1

= 12

TU = 12 units

ST = x + 7

= 13 + 7

= 20 units

SU = 20 + 12

= 32 units