Transcript Glencoe Geometry

Over Lesson 1–2
What is the value of x and AB if B is between A and
C, AB = 3x + 2, BC = 7, and AC = 8x – 1?
A. x = 2, AB = 8
B. x = 1, AB = 5
C.
D. x = –2, AB = –4
Over Lesson 1–2
What segment is congruent
to MN?
A. MQ
B. QN
C. NQ
D. no congruent segments
Over Lesson 1–2
What segment is congruent
to NQ?
A. MN
B. NM
C. QM
D. no congruent segments
Over Lesson 1–2
A. 5
B. 6
C. 14
D. 18
You graphed points on the coordinate plane.
• Find the distance between two points.
• Find the midpoint of a segment.
• distance
• irrational number
• midpoint
• segment bisector
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.
Can distance ever be negative?
Use the number line to find AX.
A. 2
B. 8
C. –2
D. –8
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 Distance on a Coordinate Plane
Check Graph the ordered pairs
and check by using the
Pythagorean Theorem.
Find Distance on a Coordinate Plane
.
Find the distance between A(–3, 4) and M(1, 2).
A. 4
B.
C.
D.
1. Add the x’s and divide by 2
2. Add the y’s and divide by 2
Assignment Day 1
p. 31, 13-31 odd
No work, No credit!
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
Find Midpoint on a Number Line
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
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.
Find the Coordinates of an Endpoint
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)
Use Algebra to Find Measures
Understand
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.
Use Algebra to Find Measures
Plan
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.
Use Algebra to Find Measures
Original measure
Use Algebra to Find Measures
Check
QR = 6 – 3x
Original Measure
Use Algebra to Find Measures
Multiply.
Simplify.
A. 1
B. 10
C. 5
D. 3
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, 33-55 odd
No work, No credit