Warm-Up Exercises
1. Find a point between A(–3, 5) and B(7, 5).
ANSWER
Sample: (2, 5)
2. Find the average of –11 and 5.
ANSWER
–3
Warm-Up Exercises
3. Solve x + 7 = 5.
2
ANSWER
3
4. Find √30 to the nearest hundredth.
ANSWER
5.48
Warm-Up Exercises
5. Find √5 + √20 to the nearest hundredth.
ANSWER
6.71
Warm-Up1Exercises
EXAMPLE
Find segment lengths
Skateboard
In the skateboard design, VW bisects XY at point T,
and XT = 39.9 cm. Find XY.
SOLUTION
Point T is the midpoint of XY .
So, XT = TY = 39.9 cm.
XY = XT + TY
Segment Addition Postulate
= 39.9 + 39.9 Substitute.
Add.
= 79.8 cm
Warm-Up2Exercises
EXAMPLE
Use algebra with segment lengths
ALGEBRA Point M is the midpoint
of VW . Find the length of VM .
SOLUTION
STEP 1
Write and solve an equation. Use the fact
that VM = MW.
VM = MW
4x – 1 = 3x + 3
x–1=3
x=4
Write equation.
Substitute.
Subtract 3x from each side.
Add 1 to each side.
Warm-Up2Exercises
EXAMPLE
Use algebra with segment lengths
STEP 2
Evaluate the expression
for VM when x = 4.
VM = 4x – 1 = 4(4) – 1 = 15
So, the length of VM is 15.
Check: Because VM = MW, the length of MW should be
15. If you evaluate the expression for MW, you should
find that MW = 15.
MW = 3x + 3 = 3(4) +3 = 15
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
In Exercises 1 and 2, identify the segment bisector
of PQ . Then find PQ.
1.
ANSWER
3
MN; 3 4
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
In Exercises 1 and 2, identify the segment bisector
of PQ . Then find PQ.
2.
ANSWER
5
line l ; 11
7
Warm-Up3Exercises
EXAMPLE
Use the Midpoint Formula
a.
FIND MIDPOINT The endpoints of RS are R(1,–3)
and S(4, 2). Find the coordinates of the midpoint M.
Warm-Up3Exercises
EXAMPLE
Use the Midpoint Formula
SOLUTION
a.
FIND MIDPOINT Use the Midpoint Formula.
4,– 3 + 2
M 1+
2
2
ANSWER
= M 52 , – 1
2
The coordinates of the midpoint M
are 5 – 1
, 2
2
Warm-Up3Exercises
EXAMPLE
Use the Midpoint Formula
b.
FIND ENDPOINT The midpoint of JK is M(2, 1). One
endpoint is J(1, 4). Find the coordinates of
endpoint K.
Warm-Up3Exercises
EXAMPLE
Use the Midpoint Formula
SOLUTION
FIND ENDPOINT Let (x, y) be the
coordinates of endpoint K. Use the
Midpoint Formula.
STEP 1
Find x.
1+ x = 2
2
1+x=4
x=3
ANSWER
STEP 2 Find y.
4+ y 1
=
2
4+y=2
y=–2
The coordinates of endpoint K are (3, – 2).
Warm-Up
Exercises
GUIDED
PRACTICE
3.
The endpoints of AB are A(1, 2) and B(7, 8). Find
the coordinates of the midpoint M.
ANSWER
4.
for Example 3
(4,5)
The midpoint of VW is M(– 1, – 2). One endpoint
is W(4, 4). Find the coordinates of endpoint V.
ANSWER (– 6, – 8)
Warm-Up4Exercises
EXAMPLE
Standardized Test Practice
SOLUTION
Use the Distance Formula. You
may find it helpful to draw a
diagram.
Warm-Up4Exercises
EXAMPLE
Standardized Test Practice
RS =
2
2
(x 2– x1) + (y 2 – y1)
Distance Formula
=
[(4 – 2)] 2+ [(–1) –3] 2 Substitute.
=
(2) + (–4 )
2
2
Subtract.
=
4+16
Evaluate powers.
=
20
Add.
~
= 4.47
Use a calculator to
approximate the square root.
ANSWER The correct answer is C.
Warm-Up
Exercises
GUIDED
PRACTICE
5.
for Example 4
In Example 4, does it matter which ordered pair
you choose to substitute for (x1, y1) and which
ordered pair you choose to substitute for (x2 , y2)?
Explain.
SAMPLE ANSWER
No, when squaring the differences in the
coordinates, you get the same answer as long as
you choose the x and y values from the same point.
Warm-Up
Exercises
GUIDED
PRACTICE
6.
for Example 4
What is the approximate length of AB , with
endpoints A(–3, 2) and B(1, –4)?
6.1 units
ANSWER
B
7.2 units
8.5 units
10.0 units
Daily
Homework
Quiz
Warm-Up
Exercises
1.
AB bisects CD at E. If CE =2
ANSWER
2.
1
in., Find CD.
4
4 1 in.
2
Point M is the midpoint of XY. Find XM.
ANSWER
17
Daily
Homework
Quiz
Warm-Up
Exercises
3.
Point M is the midpoint of PQ with endpoints
P(2, – 6 ) and Q(– 8, 0). Find the coordinates of M.
ANSWER
4.
(–3, –3)
The midpoint of GH is M(4, –1). One endpoint is
G(5, 3) . Find the coordinates of H.
ANSWER
(3, –5)
Daily
Homework
Quiz
Warm-Up
Exercises
5.
To find the distance between the swing and the
sandbox in his backyard, Darren made a graph
and found the coordinates of the swing to be (7, 2)
and the coordinates of the sandbox to be (– 3, 8).
Find the distance between the swing and the
sandbox to the nearest tenth of a unit.
ANSWER
11.7