Respuesta :

If T is the Midpoint of line SU the the values of ST, TU, and SU are;

ST= 80

TU =80

SU= 160

Further Explanation

Line segment

A line segment is a piece of a line that has two endpoints.

A ray

It is a part of a line with one end point and proceeds on in one direction.

A line

  • A line refers to collection of line along a straight path proceeding in opposite directions with no endpoints.

Mid-point

  • Mid-point is a point on a given line that divides it into two equal parts.
  • Mid-point can be calculated by the formula;

Mid point =[tex](\frac{(x_{1}+ x_{2}) }{2}, \frac{(y_{1}+ y_{2}) }{2})[/tex]

Where; [tex](x_{1},y_{1}), (x_{2},y_{2})[/tex]are co-ordinates of the endpoints of the line.

Therefore;

In this case;

If T is the mid-point of SU then;

ST is equal to TU

But; [tex]ST = 5x \\TU = 3x +32[/tex]

Hence;

[tex]5x = 3x +32[/tex]

Putting like terms together

[tex]2x = 32[/tex]

Dividing both sides by 2

[tex]x = 16[/tex]

Therefore;

The value of x = 12 cm

But;

[tex]ST = 5x\\ = 5(16) \\= 80[/tex]

[tex]TU = 3x +32 \\=3(16) +12\\=80[/tex]

        

Therefore;

ST = 80

TU = 80 and

SU = 160 units

Keywords: Mid-point,formula for mid point

Learn more about;

  • Midpoint; https://brainly.com/question/10772249
  • A segment; https://brainly.com/question/10772249
  • A ray; https://brainly.com/question/10772249
  • Example on midpoint: https://brainly.com/question/10772249

Level; High school

Subject: Mathematics

Topic: Vectors

Sub-topic: Midpoint

facundo3141592

For a given segment, the midpoint is the point that divides the segment in two halves. Knowing this we will get:

  • ST = 80
  • TU = 80
  • SU = 160

So if T is the midpoint of SU, then we will have that:

ST = TU

And we have expressions for these measures:

ST = 5*x

TU = 3*x + 32

Then we can write:

5*x = 3*x + 32

Now we can solve this for x.

5*x - 3*x = 32

2*x = 32

x = 32/2 = 16

x = 16

Now that we know the value of x, we can replace it in the equations to find the length of each segment:

ST = 5*x = 6*16 = 80

TU = 3*x + 32 = 3*16 + 32 = 80

SU = ST + TU = 80 + 80 = 160

So the correct option is the second one.

If you want to learn more, you can read:

https://brainly.com/question/4747771

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