Pythagorean Theorem, Distance Formula and Midpoint Formula · Theorem, Distance Formula and...
Transcript of Pythagorean Theorem, Distance Formula and Midpoint Formula · Theorem, Distance Formula and...
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Pythagorean Theorem, Distance
Formula and Midpoint Formula
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Pythagorean Theorem
2 2 2leg leg hyp
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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.
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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.
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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.
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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.
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11, yx 22 , yx
2 2
2 1 2 1( ) ( )D x x y y
The Distance Formula
Given two points:
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Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths.
D 3.16
2
12
2
12 )()(D yyxx
22 )43()12(D
22 )1()3(D
19D
10D
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Example
Find the distance between the points, (10, 5) and (40, 45). Round to the nearest hundredths.
2
12
2
12 )()(D yyxx
22 )545()1040(D
22 )40()30(D
1600900D
2500D
D = 50
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3. Find the distance between the points.
Round to the nearest tenths.
( ) ( )4 1 2 02 2
9 4
13
212
2
12 yyxx
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4. Find the distance between the points.
Round to the nearest tenths.
212
2
12 yyxx
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Midpoint Given 2 ordered pairs, it’s
the
AVG of the x’s and
AVG of the y’s.
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Midpoint Formula
1 2 1 2,2 2
x x y y
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Find the midpoint.
1. (3, 7) and (-2, 4)
2. (5, -2) and (6, 14)
(.5, 5.5)
(5.5, 6)
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Find the midpoint.
3. (3, -9) and (14, 16)
4. (12, 17) and (-7, 9)
(8.5, 3.5)
(2.5, 13)
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Find the midpoint. 5.
(2, 3)
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Find the midpoint. 6.
(1.5, 4)
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Given the midpt and one endpt, find the other endpt.
7. Midpt (3, -6)
Endpt (7, -3) (-1, -9)
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Given the midpt and one endpt, find the other endpt.
8. Midpt (-1, 2)
Endpt (3, 0) (-5, 4)
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Given the midpt and one endpt, find the other endpt.
9. Midpt (-4, 6)
Endpt (2, 1) (-10, 11)