1.3 midpoint + distance.notebook
September 03, 2015
9/3/15 ­ Warm Up Problem
1. What is the length of AB?
B(2,7)
2. What is the slope of AB?
A(­6,­5)
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1.3 midpoint + distance.notebook
September 03, 2015
Section 1.3 ­ Distance and Midpoint Formulas
Goals: Find coordinates of midpoints and partition segments according to a given ratio
Midpoints in the Coordinate Plane
Midpoint: the point halfway between the endpoints of the segment
Estimate the midpoint of the segment.
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1.3 midpoint + distance.notebook
September 03, 2015
The Midpoint Formula
The coordinates of the midpoint of a segment whose endpoints have coordinates (x1,y1) and (x2,y2) are
(
x1 + x2 , y1 + y2
2 2
)
Find the coordinates of the midpoint.
A (­3,3) and B (2,­4)
A
B
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1.3 midpoint + distance.notebook
September 03, 2015
Find the coordinates of the midpoint of GH for
G (8,­6) and H (­14,12)
(
x1 + x2 , y1 + y2
2 2
)
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1.3 midpoint + distance.notebook
September 03, 2015
Finding an Endpoint
The midpoint of AB is M(3,4). One endpoint is A(-3,-2).
Find the coordinates of the other endpoint B.
*Use the midpoint formula
*Fill in the variables x and y for the
coordinates of point B.
M
A
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1.3 midpoint + distance.notebook
September 03, 2015
Try it on your own...
The midpoint of XY has coordinates (4,-6).
X has coordinates (2,-3). Find the coordinates of Y.
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1.3 midpoint + distance.notebook
September 03, 2015
Partitioning a Segment
Find the coordinates of point P that lies on the directed
line segment from A(-2,1) to B(8,6) and partitions the
segment in the ratio 2 to 3.
1. Convert ratio into a fraction
2 to 3 ratio =
2. Determine the rise and run
rise = run =
3. Calculate the needed portion
of the rise and the run
4. Add calculated rise and run to
endpoint to get new coordinates.
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1.3 midpoint + distance.notebook
September 03, 2015
Assignment:
1.3 Worksheet
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