The Distance Formula...The Distance Formula Example Find the distance between (1, 4) and (-2, 3)....
Transcript of The Distance Formula...The Distance Formula Example Find the distance between (1, 4) and (-2, 3)....
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11, yx 22 , yx
2 2
2 1 2 1( ) ( )D x x y y
The Distance Formula
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Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths.
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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.
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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.
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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.
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4. Find the distance between the points.
Round to the nearest tenths.
212
2
12 yyxx
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Pythagorean Theorem
2 2 2leg leg hyp
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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
• Ashley travels 42 miles east, then 19
miles south. How far is Ashley from
the starting point? Round to the
nearest tenths.
x = 46.1 miles
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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 square has a diagonal with length of
20 cm. What is the measure of each
side? Round to the nearest tenths.
x = 14.1 cm
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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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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.
x = 10.4 cm
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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)
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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)
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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.
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Find the midpoint. 5.
(2, 3)
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Find the midpoint. 6.
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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)
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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)
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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)
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Given the midpt and one endpt, find the
other endpt. 9.
Midpt (-4, 6)
Endpt (2, 1) (-10, 11)
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Partition Line
Segments (1 Dimension)
1 2 1( )
ax x x
a b
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Partition – 1 Dimension
P is at 1, and Q is at 7.
Find the point, T, so that T partitions P to Q in a 2:1 ratio.
1 2 1
( )a
x x xa b
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Partition – 1 Dimension
C is at -6 and D is at 4.
Find the point, T, so that T is C to D in a 2:3 ratio.
1 2 1
( )a
x x xa b
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Partition – 2 Dimension
Given the points A(-2,4) and
B(7,-2), find the coordinates of the
point P on the directed line segment
AB that partitions AB in the ratio
1:2.
1 2 1
( )a
x x xa b