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cGraw
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ompanies, Inc.
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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
Less
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2nd Pass
Chapter 1 19 Glencoe Geometry
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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A B
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Copyright ©
Glencoe/M
cGraw
-Hill, a division of The M
cGraw
-Hill C
ompanies, Inc.
NAME DATE PERIOD
Chapter 1 20 Glencoe Geometry
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
Find the coordinates of the midpoint of a segment with the given endpoints.
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
Find P on −−− NM that is the given fractional distance from N to M.
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.
23. Find C on −− AB such that the ratio of AC to CB is 1:3.
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/McG
raw
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PDF Pass
Chapter 1 21 Glencoe Geometry
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
Find the coordinates of the midpoint of a segment with the given endpoints.
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
Find P on −−− NM that is the given fractional distance from N to M.
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.
23. Find C on −− AB such that the ratio of AC to CB is 1:2.
24. Find C on −− AB such that the ratio of AC to CB is 4:3.
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4
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