lesson 1.3 distance and midpoints
DESCRIPTION
Lesson 1.3 Distance and Midpoints. Geometry CP Mrs. Mongold. Chapter 1 Foldable Flap 2. Distance Formulas Number Line. -3. 4. P. Q. Chapter 1 Foldable Flap 2. Distance Formulas Cont… Coordinate Plane - PowerPoint PPT PresentationTRANSCRIPT
Chapter 1 Foldable Flap 2
• Distance Formulas Cont…– Coordinate Plane
• The distance d between two points with coordinates and
),( 11 yx),( 22 yx
2122
12 yyxxd
Answer
The coordinates of Q and R are –6 and –3.
QR = | –6 – (–3) | Distance Formula
= | –3 | or 3 Simplify.
Answer
• The coordinates are E(-4, 1) and F(3, -1)• Label them
2122
12 yyxxd
),)(,(
)1,3)(1,4(
2211 yxyx
22 11)4(3 d
22 27 d
53449 d
Answer
• The coordinates are A(-3, 4) and M(1, 2)• Label (-3, 4) and (1, 2), and
1
),( 11 yx ),( 22 yx
2122
12 yyxxd
22 42)3(1 d
22 24 d
20416 d
52d
Chapter 1 Foldable Flap 3
• Midpoint Formulas– Number Line
• The coordinate of the midpoint of a segment with endpoints that have coordinates a and b is
2
ba
Chapter 1 Foldable Flap 3
• Coordinate Plane– The coordinates of the midpoint of a segment with
endpoints that have coordinates and ),( 11 yx ),( 22 yx
2
,2
2121 yyy
xxx mm
Midpoint Examples
• The coordinates on a number line Y and O are 7 and -15 respectively. Find the coordinate of the midpoint of segment YO.
What about working backwards?
• Find the coordinates of D if E(-6, 4) is the midpoint of segment DF and F(-5, -3)
Answer
• Let D be• Let E be for the midpoint• Let F be • So…..
),( 11 yx),( mm yx
),( 22 yx
221 xx
xm
2
21 yyym
)5(12 1 x )3(8 1 y
17 x 111 y
The coordinates for point D are (-7, 11)
Answer
• If Q is the midpoint then segments PQ and QR are both equal to 6 – 3x
• So, 2(6 – 3x) = 14x + 2
12 – 6x = 14x + 2
10 = 20x
x = ½
PR = 14(1/2) + 2 = 7 + 2 = 9