NAME DATE PERIOD Study Guide and Intervention...Geo-SG01-03-05-846589-3-2-10 1 2 P Q Midpoint of a Segment Midpoint on a Number Line If the coordinates of the endpoints of a segment

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Chapter 1 18 Glencoe Geometry

1-3 Study Guide and InterventionLocating Points and Midpoints

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Midpoint of a Segment

Midpoint on a Number Line

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 .

Midpoint on a Coordinate Plane

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

then the coordinates of the midpoint of the segment are ( x1 + x2 − 2 , y1 + y2 −

2 ) .

Find the coordinate of the midpoint of −−

PQ .

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

If M is the midpoint of −−−

PQ , then the coordinate of M is -3 + 1 − 2 = -2 −

2 or -1.

Find the coordinates of M, the midpoint of −−− PQ , for P(-2, 4) and Q(4, 1).

M = ( x1+ x2 − 2 , y1+ y2 −

2 ) = ( -2 + 4 − 2 , 4 + 1 − 2 ) or (1, 2.5)

ExercisesUse 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

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)

Example 1

Example 2

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2nd Pass


Study Guide and Intervention (continued)Locating Points and Midpoints

1-3

Locate PointsThe 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

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 + m ⎪x2 - x1⎥

− n .

Locating Points on a Coordinate Plane

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 + m ⎪x2 - x1⎥ − n , y1 + m ⎪y2 - y1⎥

− n ) .

Find the coordinates of a point 1 − 3 of the distance from A to B.

A B

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

P19-001A-890857The coordinates of A and B are -5 and 2. If P is the point 1 −

3 of the distance from A to B,

then the coordinate of P is -5 + ⎪2-(-5)⎥

− 3 = -5 + 7 −

3 = -8 −

3 ≈ -2.7.

Find the coordinates of P, a point 1 − 4 of the distance from A(-2, -4)

to B(4, 3).

P = ( x 1 + m ⎪ x 2 - x 1 ⎥ − n , y 1 + m ⎪ y 2 - y 1 ⎥ − n ) = (-2 + ⎪4 - (-2)⎥ − 4 , -4 + ⎪3 - (-4)⎥ − 4 )

= (-2 + 6 − 4 , -4 + 7 − 4 ) or about (- 1 − 2 , -2 1 − 4 ) .

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

1. 1 − 5 2. 1 −

3 3. 2 −

3

4. 3 − 4 5. 1 −

4 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) 12. 2 −

5 ; N(-2, -1), M(8, 3)

Example 1

Example 2

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ompanies, Inc.

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Skills PracticeLocating Points and Midpoints

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

1. −−− DE 2. −−− BC

3. −−− BD 4. −−− AD


5. T(3, 1), U(5, 3) 6. J(-4, 2), F(5, -2)

Find the coordinates of the missing endpoint if P is the midpoint of −−−

NQ .

7. N(2, 0), P(5, 2) 8. N(5, 4), P(6, 3) 9. Q(3, 9), P(-1, 5)

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

10. 1 − 6 11. 2 −

3 12. 1 −

4

13. 3 − 4 14. 2 −

5 15. 1 −

5

16. 1 − 3 17. 5 −

6


18. 2 − 3 , N(-3, 1), M(2, 6) 19. 2 −

5 , N(-2, 5), M(0, -4)

20. 1 − 4 , N(-2, -1), M(8, 3) 21. 3 −

4 , N(4, 5), M(-7, 1)

Refer to the graph at the right.

22. Find C on −− AB such that the ratio of AC to CB is 2:3.


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PracticeLocating Points and Midpoints

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

1. −− RT 2. −−− QR

3. −− ST 4. −− PR


5. K(-9, 3), H(5, 7) 6. W(-12, -7), T(-8, -4)

Find the coordinates of the missing endpoint if E is the midpoint of −− DF .

7. F(5, 8), E(4, 3) 8. F(2, 9), E(-1, 6) 9. D(-3, -8), E(1, -2)

10. PERIMETER The coordinates of the vertices of a quadrilateral are R(-1, 3), S(3, 3), T(5, -1), and U(-2, -1). Find the perimeter of the quadrilateral. Round to the nearest tenth.

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

11. 1 − 3 12. 1 −

5 13. 1 −

6 14. 1 −

4

15. 3 − 5 16. 2 −

3 17. 5 −

6 18. 3 −

4


19. 3 − 4 , N(1, 7), M(9, -2) 20. 4 −

5 , N(-4, 5), M(2, -6)

21. 2 − 5 , N(-3, -4), M(6, 3) 22. 1 −

3 , N(-4, 2), M(7, 9)

Refer to the graph at the right.



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NAME DATE PERIOD Study Guide and Intervention...Geo-SG01-03-05-846589-3-2-10 1 2 P Q Midpoint of a Segment Midpoint on a Number Line If the coordinates of the endpoints of a segment