Midpoint and Fractional Distance

Midpoint Formula Lesson

Ms. Holmon

Learning Intentions

The student will be able to…

Use coordinate geometry involving midpoint formula to verify geometric properties.

Success Criteria:

I will…

Derive the midpoint formula. 

Determine the coordinates of a point that is a fractional distance along a number line in a one-dimensional system. 

Determine the coordinates of a point that is a fractional distance from one end of a line segment in a two-dimensional coordinate system.

Use fractional distance to find the midpoint in a one-dimensional and in a two-dimensional coordinate system. 

More than one way...

In Coordinate Geometry, there is more than one way to determine the midpoint of a line segment.

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What is the coordinate of A?

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What is the coordinate of D?

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What is the distance of between the 2 endpoints? (Remember a+b)

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Use the number line to find the distance of the midpoint of 

$\overline{AD}$  ? (Remember:  $\frac{A\ +\ B}{2}$  )

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Round your answer to the nearest tenth EX: 7.5 if necessary.  Use the number line to find the coordinate of the midpoint of 

$\overline{AD}$  

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Round your answer to the nearest tenth EX: 7.5 if necessary.  Use the number line to find the coordinate of the midpoint of 

$\overline{BD}$  

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Round your answer to the nearest tenth EX: 7.5 if necessary.  Use the number line to find the coordinate of the midpoint of 

$\overline{BC}$  

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Round your answer to the nearest tenth EX: 7.5 if necessary.  Use the number line to find the coordinate of the midpoint of 

$\overline{DE}$   

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What is x₁ for the endpoints? (-2,0) & (9,-1)?

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What is x₂ for the endpoints? (-2,0) & (9,-1)/

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What is the distance of the x's for the endpoints? (-2,0) & (9,-1). (Remember: x1 + x2)

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What is the midpoint of the x's for the endpoints? (-2,0) & (9,-1). (Remember:  $\frac{x_1+\ x_2}{2}$  )

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What is y₁ for the endpoints? (-2,0) & (9,-1).

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What is y₂ for the endpoints? (-2,0) & (9,-1).

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What is the distance of the y's for the endpoints? (-2,0) & (9,-1). (Remember: y1 + y2)

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What is the midpoint of the y's for the endpoints? (-2,0) & (9,-1). (Remember:  $\frac{y_1+\ y_2}{2}$  )

Multiple Choice

Find the midpoint of the line segment with endpoints (-2,0) & (9,-1).

• (1, 3)

• (3.5, -.5)

• (-.5, 3.5)

• (6, -.5)

Multiple Choice

Find the midpoint: (7, 4) (9, -1)

• (8, 1.5)

• (2,1)

• (-8, 1.5)

Multiple Choice

Find the midpoint: (2, -11) (-9, 0)

• (2, 9)

• (3.5, -5.5)

• (-3.5, -5.5)

Multiple Choice

Find the midpoint: (4, -1) (2, -7)

• (0, 5)

• (-3, -4)

• (3, -4)

Multiple Choice

Find the other endpoint of the line segment with the given endpoint A and midpoint M. Which equation is the x midpoint set to the x midpoint formula

A(-4, 2), M(8, 7)

• $$8\ =\ \frac{x_{1\ }+\ \left(-4\right)}{2}$$

• $$-4\ =\ \frac{x_{1\ }+\ \left(8\right)}{2}$$

• $$2\ =\ \frac{x_{1\ }+\ 7}{2}$$
  

• $$7\ =\ \frac{x_{1\ }+\ 2}{2}$$
  

Multiple Choice

What is the next step?

$$8\ =\ \frac{x_{1\ }+\ \left(-4\right)}{2}$$  

• Add 2

• Subtract 2

• Multiply 2

• Divide by 2

Multiple Choice

Find the other endpoint of the line segment with the given endpoint A and midpoint M. Which equation is the next simplified equation?

$$2\ \times\ 8\ =\frac{x_{1\ }+\left(-4\right)}{2}\ \times\ 2$$  

• $$16\ =\ x_{1\ }+\ \left(-4\right)$$

• $$-8\ =\ x_{1\ }+\ \left(8\right)$$

• $$4=\ x_{1\ }+\ 7$$
  

• $$14\ =\ x_{1\ }+\ 2$$
  

Multiple Choice

What is the next step?

$$16\ =\ x_{1\ }+\ \left(-4\right)$$  

• Add 4

• Subtract 4

• Multiply 4

• Divide by 4

Multiple Choice

Find the other endpoint of the line segment with the given endpoint A and midpoint M. Which equation is the next simplified equation?

$$16\ +\ 4\ =x_{1\ }+\left(-4\right)\ +4$$  

• $$20\ =\ x_{1\ }$$

• $$-4=\ x_{1\ }$$

• $$8=\ x_{1\ }$$
  

• $$18\ =\ x_{1\ }$$
  

Multiple Choice

Find the other endpoint of the line segment with the given endpoint A and midpoint M. Which equation is the y midpoint set to the y midpoint formula

A(-4, 2), M(8, 7)

• $$8\ =\ \frac{y_{1\ }+\ \left(-4\right)}{2}$$

• $$-4\ =\ \frac{y_{1\ }+\ \left(8\right)}{2}$$

• $$2\ =\ \frac{y1\ +\ 7}{2}$$
  

• $$7\ =\ \frac{y_{1\ }+\ 2}{2}$$
  

Multiple Choice

What is the next step?

$$7\ =\ \frac{y_{1\ }+\ 2}{2}$$  

• Add 2

• Subtract 2

• Multiply 2

• Divide by 2

Multiple Choice

Find the other endpoint of the line segment with the given endpoint A and midpoint M. Which equation is the next simplified equation?

$$2\ \times\ 7=\frac{x_{1\ }+\ 2}{2}\ \times\ 2$$  

• $$16\ =\ y_{1\ }+\ \left(-4\right)$$

• $$-8\ =\ y_{1\ }+\ \left(8\right)$$

• $$4=\ y_{1\ }+\ 7$$
  

• $$14\ =\ y_{1\ }+\ 2$$
  

Multiple Choice

What is the next step?

$$14\ =\ y_{1\ }+\ 2$$  

• Add 2

• Subtract 2

• Multiply 2

• Divide by 2

Multiple Choice

Find the other endpoint of the line segment with the given endpoint A and midpoint M. Which equation is the next simplified equation?

$$14\ -\ 2\ =y_{1\ }+2\ -2$$  

• $$20\ =\ y_{1\ }$$

• $$12=\ y_{1\ }$$

• $$8=\ y_{1\ }$$
  

• $$18\ =\ y_{1\ }$$
  

Multiple Choice

Find the other endpoint of the line segment with the given endpoint A and midpoint M.

A(-4, 2), M(8, 7)

• (20, 12)

• (-1, 7.5)

• (-6, -2.5)

• (1.5, -5.5)

Multiple Choice

Line segment AB has midpoint M. The coordinates of endpoint A(-1,2) and midpoint M (0,-3) are given. What are the coordinates of endpoint B? (HINT: draw a picture of the line and label the points)

• ( 1 , -8 )

• ( 1 , 8 )

• ( 8 , -1 )

• ( - 8 , -1 )

Multiple Choice

Point M with coordinates (3,4) is the midpoint of the line AB and A has the point (-1,6). What is the point of B?

• (1,5)

• (2,10)

• (7,2)

• (1,2)

Multiple Choice

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?

Poll

How confident do you feel about knowing where the midpoint formula came from?

• I can teach this.

• I understand but I have some questions

• I'm unsure. I need more practice.

• I have no idea what you are talking about.

Poll

How confident do you feel about determining the coordinates of a point on a number line?

• I can teach this.

• I understand but I have some questions

• I'm unsure. I need more practice.

• I have no idea what you are talking about.

Poll

How confident do you feel about determining the coordinates of a point on a coordinate plane?

• I can teach this.

• I understand but I have some questions

• I'm unsure. I need more practice.

• I have no idea what you are talking about.

Poll

How confident do you feel about finding the endpoint when you are given the midpoint and another endpoint?

• I can teach this.

• I understand but I have some questions

• I'm unsure. I need more practice.

• I have no idea what you are talking about.

Well that's all folks

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