Download presentation

Published byJarrett Eccles Modified over 4 years ago

1
**Investigating the Midpoint and Length of a Line Segment**

Developing the Formula for the Midpoint of a Line Segment Definition Midpoint: The point that divides a line segment into two equal parts.

2
**D C B -5 + 3 2 A = -1 MAB = (-1, 4) 6 + (-4) 2 = 1**

A. Graph the following pairs of points on graph paper. Connect points to form a line segment. Investigate ways to find the midpoint of the segment. Write the midpoint as an ordered pair. a) A(-5, 4) and B(3, 4) b) C(1, 6) and D(1, -4) -5 + 3 2 D C A B = -1 MAB = (-1, 4) 6 + (-4) 2 = 1 MCD = (1, 1)

3
**Describe how you found the midpoint of each line segment.**

To find midpoint of AB, add x-coordinates together and divide by 2 To find midpoint of CD, add y-coordinates together and divide by 2

4
** H S T -4 + 2 -5 + 3 2 2 = -1 = -1 MGH = (-1, -1) 1 + 6**

B. Graph the following pairs of points on graph paper. Connect points to form a line segment. Find the midpoint using your procedure described in part A. If your procedure does not work, see if you can discover another procedure that will work. a) G(-4, -5) and H(2, 3) b) S(1, 2) and T(6, -3) -4 + 2 2 -5 + 3 2 = -1 = -1 G H T S MGH = (-1, -1) 1 + 6 2 2 + (-3) 2 = 7/2 = -1/2 MST = (7/2, -1/2)

5
**C. Compare your procedures and develop a formula that will work for all line segments.**

Line segment with end points, A(xA, yA) and B(xB, yB), then the midpoint is MAB = xA + xB , yA + yB

6
**1. Find the midpoint of the following pairs of points: **

D. Use the formula your group created in part C to solve the following questions. 1. Find the midpoint of the following pairs of points: a) A(-2, -1) and B(6, 3) b) C(7, 1) and D(-5, -3) c) G(0, -6) and H(9, -2) MAB = , MCD = 7 + (-5) , 1 + (-3) MAB = (2, 1) MCD = (1, -1) MGH = 0 + 9 , (-2) MGH = (9/2, -4)

7
**The other end point is B (10, 3)**

2. Challenge: Given the end point of A(-2, 5) and midpoint of (4, 4), what is the other endpoint, B. (4, 4) = -2 + xB , yB = 4 -2 + xB 2 = 4 5 + yB 2 -2 + xB = 4(2) 5 + yB = 4(2) xB = 8 + 2 yB = 8 - 5 xB = 10 yB = 3 The other end point is B (10, 3)

8
**Developing the Formula for the Length of a Line Segment**

A. Graph the following pairs of points on graph paper. Connect points to form a line segment. Investigate ways to find the length of the each segment. a) A(-5, 4) and B(3, 4) b) C(1, 6) and D(1, -4) D C 3 – (-5) = 8 units A B 10 units 8 units 6 – (-4) = 10 units

9
**Describe how you found the length of each line segment.**

To find length of AB, subtract the x-coordinates To find length of CD, subtract the y-coordinates

10
** H dGH2 = 62 + 82 dGH2 = 100 dGH= 100 √ 3 – (-5) = 8 units**

B. Graph the following pairs of points on graph paper. Connect points to form a line segment. Find the length using your procedure described in part B. If your procedure does not work, see if you can discover another procedure that will work. a) G(-4, -5) and H(2, 3) dGH2 = dGH2 = 100 G H dGH= 100 √ 3 – (-5) = 8 units dGH = 10 units 2 – (-4) = 6 units

11
**S T dST2 = 52 + 52 dST2 = 50 dST= 50 √ 2 – (-3) dST = 7.07 units**

b) S(1, 2) and T(6, -3) dST2 = dST2 = 50 T S dST= 50 √ 2 – (-3) = 5 units dST = 7.07 units 6 – 1 = 5 units

12
**C. Compare your procedures and develop a formula that will work for all line segments.**

Line segment with end points, A(xA, yA) and B(xB, yB), then the length is dAB2 = (xB – xA)2 + (yB – yA)2 dAB = √(xB – xA)2 + (yB – yA)2

13
**E. Use the formula your group created in part D to solve the following questions.**

1. Find the midpoint of the following pairs of points: a) A(-2, -1) and B(6, 3) b) C(7, 1) and D(-5, -3) c) G(0, -6) and H(9, -2) dAB = √(6+2)2 +(3+1)2 dCD = √(-5–7)2 + (-3–1)2 dAB= 80 √ dCD= 160 √ dAB = 8.94 units dCD = units dGH = √(-6–0)2 +(-2+6)2 dGH= 52 √ dGH= 7.21 units

14
**Store F should receive the call.**

2. Challenge: A pizza chain guarantees delivery in 30 minutes or less. The chain therefore wants to minimize the delivery distance for its drivers. a) Which store should be called if a pizza is to be delivered to point P(6, 2) and the stores are located at points D(2, -2), E(9, -2), F(9, 5)? dDP = √(6-2)2 +(2+2)2 dEP = √(6–9)2 + (2+2)2 dDP = √ dEP= 25 √ dEP = 5.66 units dEP = 5 units dFP = √(6–9)2 +(2-5)2 Store F should receive the call. dFP= 18 √ dFP= 4.24 units

15
**c) Find a point that would be the same distance from two of these stores.**

MDF = 2 + 9 , MDE = 2 + 9 , -2 – 2 MDE = (11/2, -2) MDF = (11/2, 3/2) MEF = 9 + 9 , MEF = (9, 3/2)

Similar presentations

OK

Warm Up C. Warm Up C Objectives Use the Distance Formula and the Pythagorean Theorem to find the distance between two points.

Warm Up C. Warm Up C Objectives Use the Distance Formula and the Pythagorean Theorem to find the distance between two points.

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google