NAME DATE PERIOD 1-3 Study Guide and Intervention - Georgetown ISD

[Pages:2]NAME

DATE

1-3 Study Guide and Intervention

Locating Points and Midpoints

Midpoint of a Segment

PERIOD

Midpoint on a Number Line

Midpoint on a Coordinate Plane

If the coordinates of the endpoints of a segment are x1 and x2, then the coordinate of the midpoint of the segment is x1 + x2 .

2

If a segment has endpoints with coordinates (x1, y1) and (x2, y2),

( ) then the coordinates of the midpoint of the segment are x1 + x2 , y1 + y2 .

2

2

Example 1 Find the coordinate of the midpoint of PQ.

P

Q

-3 -2 -1 0 1 2

The coordinates of P and Q are -3 and 1.

If MGeios-tShGe 0m1i-d0p3o-i0n5t-o8f4P6Q58, 9then the coordinate of M is

-3 + 1 2

=

-2 2

or -1.

Example 2 Find the coordinates of M, the midpoint of PQ, for P(-2, 4) and

Q(4, 1).

( ) ( ) M =

x1+ x2 , y1+ y2

2

2

=

-2

+ 2

4

,

4 + 1 2

or (1, 2.5)

Exercises

Use the number line to find the coordinate of the midpoint of each segment.

1. CE

2. DG

3. AF

4. EG

5. AB

6. BG

7. BD

8. DE

AB C

D EF

G

?10 ?8 ?6 ?4 ?2 0 2 4 6 8

Geo-SG01-03-06-846589

Find the coordinates of the midpoint of a segment with the given endpoints.

9. A(0, 0), B(12, 8)

10. R(-12, 8), S(6, 12)

11. M(11, -2), N(-9, 13)

12. E(-2, 6), F(-9, 3)

13. S(10, -22), T(9, 10)

14. K(-11, 2), L(-19, 6)

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 1

18

Glencoe Geometry

NAME

DATE

PERIOD

1-3 Study Guide and Intervention (continued)

Locating Points and Midpoints

Locate Points

The midpoint of a segment is half the distance from one endpoint to the other. Points located at other fractional distances from one endpoint can be found using a similar method.

Locating Points on a Number Line

Locating Points on a Coordinate Plane

If

the

coordinates

of

the

endpoints

of

a

segment

are

x1

and

x2

and

the

point

is

m n

of

the

distance from x1 to x2, then the coordinate of the point is x1 +

mx2 - x1 n

.

If

a

segment

has

endpoints

A(x1,

y1)

and

B(x2,

y2)

and

the

point

is

m n

of

the

distance

from

( ) point A to point B, then the coordinates of the point are

x1

+

mx2 - x1 n

,

y1 +

my2 - y1 n

.

Example 1

A

Find

the

coordinates

of

a

point

1 3

of

the

distance

from

A

to

B.

B

-6 -5 -4 -3 -2 -1 0 1 2 3 4

The coordinates of A and B are -5 and 2.

P19-001A-890857 then the coordinate of P is -5 +

2-(-5) 3

If P is = -5

the

+

7 3

point

1 3

=

-8 3

of the distance -2.7.

from

A

to

B,

Example 2 to B(4, 3).

Find

the

coordinates

of

P,

a

point

1 4

of

the

distance

from

A(-2,

-4)

( ) ( ) P =

x1 +

mx2 - x1 n

, y1 +

my2 - y1 n

=

-2 +

4

- (-2) 4

,

-4

+

3 - (-4) 4

( ) ( ) =

-2

+

6 4

,

-4

+

7 4

or about

-

1 2

,

-2

1 4

.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 1-3

Exercises

Use the number line to find the coordinate of the point the given fractional distance from A to B.

1.

1 5

2.

1 3

4.

3 4

5.

1 4

A

B

?10 ?8 ?6 ?4 ?2 0 2 4 6 8 10

P19-0032.A23-890857

6.

2 5

Find P on NM that is the given fractional distance from N to M.

7.

1 5

;

N(-3,

-2),

M(1,

1)

8.

1 3

;

N(-2,

-4),

M(4,

4)

9.

2 3

;

N(-7,

3),

M(5,

2)

10.

3 4

;

N(-3,

1),

M(2,

6)

11.

1 4

;

N(-2,

5),

M(0,

-4)

Chapter 1

12.

2 5

;

N(-2,

-1),

M(8,

3)

19

Glencoe Geometry

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