Download Lesson 1-3 - Elgin Local Schools

Lesson
1-3
Distance and Midpoints
Ohio Content Standards:
Ohio Content Standards:
• Estimate, compute and
solve problems
involving scientific
notation, square roots
and numbers with
integer exponents.
Ohio Content Standards:
• Apply order of
operations to simplify
expressions and
perform computations
involving integer
exponents and radicals.
Distance Formula
Distance Formula
• Number Line
Distance Formula
• Number Line
P
Q
a
b
Distance Formula
• Number Line
P
Q
a
b
» PQ = l b – a l or l a – b l
Distance Formula
Distance Formula
• Coordinate Plane
Distance Formula
• Coordinate Plane
– The distance d between
two points with
coordinates (x1, y1) and
(x2, y2) is given by
Distance Formula
• Coordinate Plane
– The distance d between
two points with
coordinates (x1, y1) and
(x2, y2) is given by
x
 x1   y 2  y1
2
2
2
Use the number line to find QR.
Use the number line to find QR.
Q
-8
-7
-6 -5
R
-4
-3
-2
-1
0
Find the distance between
E(-4, 1) and F(3, -1).
Midpoint
Midpoint
• Number Line
Midpoint
• Number Line
P
Q
a
b
Midpoint
• Number Line
P
Q
a
b
»
ab
2
Midpoint
Midpoint
• Coordinate Plane
Midpoint
• Coordinate Plane
– The coordinates of the
midpoint of a segment
whose endpoints have
coordinates (x1, y1) and
(x2, y2) are
Midpoint
• Coordinate Plane
– The coordinates of the
midpoint of a segment
whose endpoints have
coordinates (x1, y1) and
(x2, y2) are  x1  x2 , y1 

2
y2 

2

The coordinates on a number
line of J and K are -12 and
16, respectively. Find the
coordinate of the midpoint of
JK.
Find the coordinates of the
midpoint of GH for G(8, -6)
and H(-14, 12).
Find the coordinate of D if
E(-6, 4) is the midpoint of DF
and F has coordinates (-5, -3).
What is the measure of PR if Q
is the midpoint of PR?
P
Q
R
Assignment:
Pgs. 25 - 27
14 - 44 evens
58 - 68 evens