Question

Since we know U is the midpoint, we can say TU equals BLANK? Substituting in our values for each we get BLANK? =12x - 1

Answer 1

Since we know U is the midpoint, we can say TU equals UV. Substituting in our values for each we get 35 units.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since U is the midpoint of line segment TV, we can logically deduce the following:

TV = TU + UV

Line segment TU = Line segment UV

8x + 11 = 12x - 1

4x = 12

x = 3 units.

For line segment TU, we have;

TU = 8x + 11

TU = 8(3) + 11

TU = 35 units.

Answer 2

x = 3

Length of each segment = 3

Explanation:

Since point U is the midpoint of the line segment TV, that means both the parts of the segment UV and TU will be equal in measure.

m(TU) = m(VU)

(8x + 11) = (12x - 1)

By further solving this,

8x + 11 + 1 = 12x - 1 + 1

8x + 12 = 12x

8x + 12 - 8x = 12x - 8x

12 = 4x

x =
`(12)/(4)`

x = 3

(12x - 1) = 12×3 - 1

= 35

And the length of each segment will be 35 units.