1.3 Notes: Midpoint & Distance Formulas

Presentation

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Mathematics

•

9th Grade

•

Medium

•

CCSS

HSG.GPE.B.6, HSG.GPE.B.7, 6.NS.C.6B

Standards-aligned

Eric Swank

Used 351+ times

FREE Resource

6 Slides • 11 Questions

Midpoint & Distance

We use the midpoint formula to find the point that lies between 2 points on a line.

We use the distance formula to find the distance between 2 points.

Review: Graphing in the coordinate plane

Multiple Choice

Where is point A located?

( 7 , 2 )

( 2 , 6 )

( - 2 , 7 )

( 2 , 7 )

Multiple Choice

Where is point E located?

( 2, 0 )

( 2 , 2 )

( 0 , 2 )

( 0 , 0 )

Fill in the Blanks

Find the midpoint between the points on the graph. Write your answer as an ordered pair. Do not put spaces between the coordinates. EX: (5,6)

Type answer...

Fill in the Blanks

Find the midpoint between the points on the graph. Write your answer as an ordered pair.

Type answer...

Midpoint

To find the midpoint of 2 points, plug in your points into the given formula.
Simplify your answer to get the coordinate that lies directly in the middle of the 2 points.

Find the midpoint of the points (-3,3) & (5,3).

To find the midpoint,

1. Plug in (-3) for X₁ and plug in (3) for Y₁.

2. Plug in (5) for X₂ and plug in (3) for Y₂.

3. Simplify your answer to find the coordinate that lies between the two points.

Multiple Choice

What is the midpoint between (3,-1) and (7,-5)?

(5,-2)

(5,-3)

(10,-6)

(2,-2)

Multiple Choice

What is the midpoint between (4,12) and (-6,14)?

(-1,13)

(13,-1)

(13,1)

(5,13)

Multiple Choice

Find the midpoint of the segment with the endpoints:(4, 12) and (-6, 14)

(-1, 13)

(13, 1)

(13, -1)

(5, 13)

Distance Formula

To find the distance between two points, plug in the x and y values into the formula given.
Simplify your answer so that you can find the distance (d) between the two points.

Find the distance between the points (0,0) and (6,8).

To find the distance:

1. Plug in (6) for X₂ and (0) for X₁.

2. Plug in (0) for Y₂ and (0) for Y₁.

3. Simplify your answer to find d.

Multiple Select

Which of the following shows the correct way to insert the following coordinates into the DIstance Formula?

(3, 4) , (7, 1)

$d\ =\ \sqrt{\left(4\ -\ 3\right)^2\ +\ \left(7\ -\ 1\right)2}$

$d\ =\ \sqrt{\left(7\ -\ 3\right)^2\ +\ \left(1\ -\ 4\right)^2}$

$d\ =\ \sqrt{\left(7\ -\ 4\right)^2\ +\ \left(1\ -\ 3\right)^2}$

$d\ =\ \sqrt{\left(3\ -\ 7\right)^2\ +\ \left(4\ -\ 1\right)^2}$

$d\ =\ \sqrt{\left(3\ +\ 7\right)^2\ -\ \left(4\ +\ 1\right)^2}$

Multiple Choice

Find the distance between the points (5, 7) and (-2, -2).

5.7

5.8

8.6

11.4

Multiple Choice

Find the distance between (0, 10) and (12, 1).

Multiple Choice

What is the distance between AB?

Midpoint & Distance

We use the midpoint formula to find the point that lies between 2 points on a line.

We use the distance formula to find the distance between 2 points.

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