the distance formula...the distance formula example find the distance between (1, 4) and (-2, 3)....
TRANSCRIPT
11, yx 22 , yx
2 2
2 1 2 1( ) ( )D x x y y
The Distance Formula
Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths.
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
Example
Find the distance between the points, (10, 5) and (40, 45). Round to the nearest hundredths.
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
3. Find the distance between the points.
Round to the nearest tenths.
3. Find the distance between the points.
Round to the nearest tenths.
( ) ( )4 1 2 02 2
9 4
13
212
2
12 yyxx
4. Find the distance between the points.
Round to the nearest tenths.
4. Find the distance between the points.
Round to the nearest tenths.
212
2
12 yyxx
Pythagorean Theorem
2 2 2leg leg hyp
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
• 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
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 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
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.
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
Midpoint Given 2 ordered pairs, it’s
the
AVG of the x’s and
AVG of the y’s.
Midpoint Formula
1 2 1 2,2 2
x x y y
Find the midpoint.
1. (3, 7) and (-2, 4)
2. (5, -2) and (6, 14)
Find the midpoint.
1. (3, 7) and (-2, 4)
2. (5, -2) and (6, 14)
(.5, 5.5)
(5.5, 6)
Find the midpoint.
3. (3, -9) and (14, 16)
4. (12, 17) and (-7, 9)
Find the midpoint.
3. (3, -9) and (14, 16)
4. (12, 17) and (-7, 9)
(8.5, 3.5)
(2.5, 13)
Find the midpoint. 5.
Find the midpoint. 5.
(2, 3)
Find the midpoint. 6.
Find the midpoint. 6.
(1.5, 4)
Given the midpt and one endpt, find the
other endpt. 7.
Midpt (3, -6)
Endpt (7, -3)
Given the midpt and one endpt, find the
other endpt. 7.
Midpt (3, -6)
Endpt (7, -3) (-1, -9)
Given the midpt and one endpt, find the
other endpt. 8.
Midpt (-1, 2)
Endpt (3, 0)
Given the midpt and one endpt, find the
other endpt. 8.
Midpt (-1, 2)
Endpt (3, 0) (-5, 4)
Given the midpt and one endpt, find the
other endpt. 9.
Midpt (-4, 6)
Endpt (2, 1)
Given the midpt and one endpt, find the
other endpt. 9.
Midpt (-4, 6)
Endpt (2, 1) (-10, 11)
Partition Line
Segments (1 Dimension)
1 2 1( )
ax x x
a b
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
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
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