Transcript The Distance Formula & Pythagorean Theorem Learning Target: Students can find the distance between 2 points using the distance formula.

The Distance Formula &
Pythagorean Theorem
Learning Target:
Students can find the distance between 2
points using the distance formula.
Review the HW
The Distance Formula
 x2 , y 2 
x1 , y1 
D
(x

x
)

(
y

y
)
2
1
2
1
2
2

Example
Find the distance between (1, 4) and (-2, 3).
Round to the nearest hundredths.
D
D
D
D
( x
2
2

x
)

(
y

y
)
2
1
2
1

(2  1)  (3  4) 
(3)  (1) 
2
2
9 1
10
D
D = 3.16
2
2
Example
Find the distance between the points, (10, 5) and
(40, 45). Round to the nearest hundredths.
D
D
D
D
D
( x  x )  ( y  y ) 
(40  10)  (45  5) 
(30)  (40) 
2
2
2
1
2
2
2
2
2
9001600
2500
D = 50
1
3. Find the distance between the points.
Round to the nearest tenths.
x2  x1    y2  y1 
2
2
(4  1)  ( 2  0)
2
94
13
2
4. Find the distance between the points.
Round to the nearest tenths.
x2  x1    y2  y1 
2
2
Pythagorean Theorem
leg  leg  hyp
2
2
2
Pythagorean Theorem Word Problems
• A square has a diagonal with length of
20 cm. What is the measure of each
side? Round to the nearest tenths.
Pythagorean Theorem Word Problems
• A 25 foot ladder is leaning against a
building. The foot of the ladder is 15
feet from the base of the building.
How high is the top of the ladder
along the building? Round to the
nearest tenths.
Pythagorean Theorem Word Problems
• Ashley travels 42 miles east, then 19
miles south. How far is Ashley from
the starting point? Round to the
nearest tenths.
Pythagorean Theorem Word Problems
• What is the length of the altitude of an
equilateral triangle if a side is 12 cm?
Round to the nearest tenths.