�ݺ�ߣ

The Distance Formula
• The ______________________________ (x₁, y ₁) and (x₂, y ₂) is:
• The distance formula is based on the Pythagorean Theorem,
a2 + b2 = c2, a formula for the three sides of a right triangle.
Distance between two points

You Try!
7. A(6,7) B(-1,7) 8. E (-1,7) F(12,0)
𝑑 = (−1 − 6)2+(7 − 7)2
𝑑 = 49 + 0
d = 7
𝑑 = (12 − −1)2+(0 − 7)2
𝑑 = 169 + 49 = 218
d ≈ 14.8

You Try!
9.
You travel about _________ between platform B and C.
33.5 m.

FIND THE ERROR!
Your friend did not subtract the x-coordinates and then
the y-coordinates.
It should be: d = (3 − 1)2+(8 − 5)2= 4 + 9 ≈ 3.6

Midpoint Formulas
 On a Number Line, the
midpoint is the __________
of the coordinates of the
___________.
 In the Coordinate Plane, the
coordinates of the midpoint
are the average of the
_____________and the
average of the ____________
of the ___________.
average
x-coordinates
y-coordinates
endpoints
endpoints

Examples:
1.
2.
= 9 + -4
2
= 2.5
𝑥1 + 𝑥2
2
,
𝑦1 + 𝑦2
2
=
7 + 2
2
,
5 + −4
2
= 4.5 , 0.5
a + b
2

You Try!
1. 3 and 5 2. -7 and 4
3. A(6,7) , B(4,3) 4. A (14,-2), B (7, -8)
6+4
2
,
7+3
2
= (5, 5)
3+5
2
= 4
−7+4
2
= -1.5
14+7
2
,
−2 + −8
2
= (10.5, -5 )

Example:
3.
M=
𝑥1+𝑥2
2
,
𝑦1+𝑦2
2
Work Backwards!!!
(-2,1) =
−5+𝑥2
2
,
7 + 𝑦2
2
Split it up into x and y equations,
and solve!
-2 =
−5+𝑥2
2
1 =
7 + 𝑦2
2
Multiply each side by 2.
· 2
2 ·
-4 = −5 + 𝑥2
+ 5
+ 5
1 = 𝑥2
· 2
2 ·
2 = 7 + 𝑦2
- 7
-5 = 𝑥2
- 7
The other endpoint
is (1, -5).

You Try!
5. Y(0,2) 6. Y(-10,5)
(3, -5) =
0+𝑥2
2
,
2 + 𝑦2
2
6 = 0 + x2 -10 = 2 + y2
6 = x2 -12 = y2
(6, -12)
(3, -5) =
−10+𝑥2
2
,
5 + 𝑦2
2
6 = -10 + x2 -10 = 5 + y2
16 = x2 -15 = y2
(16, -15)

�ݺ�ߣ

UNIT 3 MAth 10 Lesson 1 and 2 Distance and midpoint formula.pdf

Recommended

More Related Content

Similar to UNIT 3 MAth 10 Lesson 1 and 2 Distance and midpoint formula.pdf (20)

More from CarljohnCallos (20)

Recently uploaded (20)

UNIT 3 MAth 10 Lesson 1 and 2 Distance and midpoint formula.pdf