Transcript 1-3 Distance and Midpoints

1-3 Distance and Midpoints
You graphed points on the coordinate plane.
• Find the distance between two points.
• Find the midpoint of a segment.
The distance between two points is the length of the
segment with those points as its endpoints.
Distance is ALWAYS positive in math.
p. 25
Find Distance on a Number Line
Use the number line to find QR.
The coordinates of Q and R are –6 and –3.
QR = | –6 – (–3) |
= | –3 | or 3
Answer: 3
Distance Formula
Simplify.
Use the number line to find AX.
A. 2
B. 8
C. –2
D. –8
Distance Formula
p. 26
You will need a scientific calculator to do this problem
1. Put x’s and y’s in the formula
2. Subtract x’s and square
3. Subtract y’s and square
4. Add numbers under the radical
5. Take square root if answer is in decimal form.
Find Distance on a Coordinate Plane
Find the distance between E(–4, 1) and F(3, –1).
(x1, y1) = (–4, 1) and
(x2, y2) = (3, –1)
Find the distance between A(–3, 4) and M(1, 2).
A. 4
B.
C.
D.
1-3 Assignment Day 1
p. 31, 13-31 odd
No work, No credit!
1-3 Distance and Midpoints Day 2
You graphed points on the coordinate plane.
• Find the distance between two points.
• Find the midpoint of a segment.
Midpoint Definition
The midpoint of a segment is the point halfway
between the end points of the segment.
A
M
B
M is the midpoint of 𝐴𝐵
𝐴𝑀 ≈ 𝑀𝐵
(reads line segment AM is congruent to line segment MB
Midpoint Formula
p. 27
1. Add the x’s and divide by 2
2. Add the y’s and divide by 2
Find Midpoint on a Number Line
DECORATING Marco places a couch so that its end is
perpendicular and 2.5 feet away from the wall. The
couch is 90” wide. How far is the midpoint of the couch
back from the wall in feet?
First we must convert 90 inches to 7.5 feet. The
coordinates of the endpoints of the couch are 2.5 and 10.
Let M be the midpoint of the couch.
Midpoint Formula
x1 = 2.5, x2 = 10
Simplify.
Answer: The midpoint of the couch back is 6.25 feet
from the wall.
DRAG RACING The length of a drag racing strip is
mile long. How many feet from the finish line is
the midpoint of the racing strip?
A. 330 ft
1 mile = 5280 feet
B. 660 ft
C. 990 ft
D. 1320 ft
Coordinate Plane Midpoint Formula
Same formula, but…
1. Use it for the x coordinates.
2. Use it for the y coordinates.
Find Midpoint in Coordinate Plane
Answer: (–3, 3)
A. (–10, –6)
B. (–5, –3)
C. (6, 12)
D. (–6, –12)
Find the Coordinates of an Endpoint
Let D be (x1, y1) and F be (x2, y2) in the Midpoint
Formula.
(x2, y2) = (–5, –3)
Write two equations to find the coordinates of D.
Midpoint Formula
Midpoint Formula
Answer: The coordinates of D are (–7, 11).
Find the coordinates of R if N (8, –3) is the midpoint
of RS and S has coordinates (–1, 5).
A. (3.5, 1)
B. (–10, 13)
C. (15, –1)
D. (17, –11)
hint:
𝑥1 +(−1)
2
=8
𝑦1 +5
2
= -3
Use Algebra to Find Measures
Understand
Plan
You know that Q is the midpoint of PR,
and the figure gives algebraic measures
for QR and PR. You are asked to find
the measure of PR.
Because Q is the midpoint, you know
that
Use this equation and the algebraic measures to find a
value for x.
Solve
Subtract 1 from each side.
Original measure
What does the word bisect mean?
Bi means:
Sector means:
two
An area or portion, subdivision
Bisect – divide into 2 equal parts
Segment Bisector
A segment bisector is any segment, line, or line
that intersects a segment at its midpoint.
Construction: Bisect a Segment
1. Draw a segment.
2. Place the compass on one end and open the compass
bigger than half of the segment.
3. Draw arcs above and below the segment.
4. Without moving the compass sixe, move the point to the
other end of the segment.
5. Draw arcs about and below the segment.
6. Use a straightedge to connect the x’s you made above and
below the segment.
7. Where this new segment crosses the 1st one is the
midpoint.
See page 30 for pictures.
Assignment 1-3
p. 31, 28-30 even, 33-41 odd, 47,49
No work, No credit