Question

If T is the midpoint of SU find the values of x, ST and SU.

Answer 1

Answer:  The required values are

x = 12 units, ST = 60 units and SU = 120 units.

Step-by-step explanation:  Given that T is the midpoint of SU, where

ST = 5x  and  TU = 3x + 24.

We are to find the values of x, ST and SU.

Since T is the midpoint of SU, so we get

$ST=TU\\\\\Rightarrow 5x=3x+24\\\\\Rightarrow 5x-3x=24\\\\\Rightarrow 2x=24\\\\\Rightarrow x=\dfrac{24}{2}\\\\\Rightarrow x=12.$

So, the value of x is 12.

Therefore,

$ST=5\times12=60$

and

$SU=5x+3x+24=8x+24=8\times12+24=96+24=120.$

Thus, the required values are

x = 12 units, ST = 60 units and SU = 120 units.

Answer 2

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

x= 12

ST= 60

SU= 120

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 =$(\frac{(x_{1} +x_{2})}{2} ), (\frac{(y_{1} +y_{2})}{2})$

Where; $((x_{1} ,y_{1}), (x_{2},y_{2})$ 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; ST = $5x$ and TU = $3x+24$

Hence;

$5x =3x+24$

Putting like terms together

$5x-3x = 24$

$2x =24$

Dividing both sides by 2

$x = 12$

Therefore;

$x = 12$

But;

$ST = 5x$

            $= 5(12)$

             $= 60$

$TU = 3x + 24$

            $= 3(12)+ 24$

            $= 36 + 24$

            $= 60$

Therefore;

ST = TU and

SU = 120 units

Keywords: Mid-point,formula for mid point

Learn more about;

Midpoint; brainly.com/question/12526212

Example on midpoint: brainly.com/question/12526212

Level; High school

Subject: Mathematics

Topic: Vectors

Sub-topic: Midpoint