1 / 19

1.3 Use midpoint and distance formulas You will find lengths of segments in the coordinate plane

1.3 Use midpoint and distance formulas You will find lengths of segments in the coordinate plane Essential question: How do you find the distance and the midpoint between two points in the coordinate plane?. Skateboard.

clive
Download Presentation

1.3 Use midpoint and distance formulas You will find lengths of segments in the coordinate plane

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 1.3 Use midpoint and distance formulas You will find lengths of segments in the coordinate plane Essential question: How do you find the distance and the midpoint between two points in the coordinate plane?

  2. Skateboard In the skateboard design, VWbisects XYat point T, and XT=39.9cm. Find XY. Point Tis the midpoint of XY . So, XT = TY = 39.9cm. EXAMPLE 1 Find segment lengths SOLUTION XY = XT + TY Segment Addition Postulate = 39.9 + 39.9 Substitute. = 79.8cm Add.

  3. ALGEBRA Point Mis the midpoint of VW. Find the length of VM . STEP 1 Write and solve an equation. Use the fact that VM = MW. EXAMPLE 2 Use algebra with segment lengths SOLUTION VM= MW Write equation. 4x–1= 3x + 3 Substitute. x – 1 = 3 Subtract 3xfrom each side. x = 4 Add 1 to each side.

  4. STEP 2 Evaluate the expression for VMwhen x =4. So, the length of VMis 15. Check: Because VM = MW, the length of MWshould be 15. If you evaluate the expression for MW, you should find that MW = 15. MW = 3x + 3 = 3(4) +3 = 15 EXAMPLE 2 Use algebra with segment lengths VM = 4x – 1 = 4(4) – 1 = 15

  5. In Exercises 1 and 2, identify the segment bisectorof PQ . Then find PQ. 1. ANSWER MN; 3 3 4 for Examples 1 and 2 GUIDED PRACTICE

  6. In Exercises 1 and 2, identify the segment bisectorof PQ . Then find PQ. 2. 5 ANSWER line l ; 11 7 for Examples 1 and 2 GUIDED PRACTICE

  7. a.FIND MIDPOINTThe endpoints ofRSare R(1,–3) and S(4, 2). Find the coordinates of the midpoint M. EXAMPLE 3 Use the Midpoint Formula

  8. SOLUTION 1 , – , M M = 2 5 a.FIND MIDPOINTUse the Midpoint Formula. 2 The coordinates of the midpoint Mare 1 5 – , 2 2 ANSWER – 3 + 2 1 + 4 2 2 EXAMPLE 3 Use the Midpoint Formula

  9. b.FIND ENDPOINTThe midpoint of JKis M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K. EXAMPLE 3 Use the Midpoint Formula

  10. STEP 1 Find x. STEP 2 Find y. 4+ y 1+ x 1 2 = = 2 2 ANSWER The coordinates of endpoint Kare (3, – 2). EXAMPLE 3 Use the Midpoint Formula SOLUTION FIND ENDPOINTLet (x, y) be the coordinates of endpoint K. Use the Midpoint Formula. 4 + y = 2 1 + x = 4 y =–2 x =3

  11. 3. The endpoints of ABare A(1, 2) andB(7, 8). Find the coordinates of the midpoint M. ANSWER (4,5) 4. The midpoint of VWis M(– 1, – 2). One endpoint is W(4, 4). Find the coordinates of endpoint V. ANSWER (– 6, – 8) for Example 3 GUIDED PRACTICE

  12. Use the Distance Formula. You may find it helpful to draw a diagram. EXAMPLE 4 Standardized Test Practice SOLUTION

  13. RS = ~ = 2 2 = (x– x) + (y–y) 2 1 2 1 = 2 2 [(4 – 2)] + [(–1) –3] = 2 2 (2) + (–4 ) = 4+16 4.47 20 ANSWER The correct answer is C. EXAMPLE 4 Standardized Test Practice Distance Formula Substitute. Subtract. Evaluate powers. Add. Use a calculator to approximate the square root.

  14. 5. In Example 4, does it matter which ordered pair you choose to substitute for (x , y ) and which ordered pair you choose to substitute for (x , y )? Explain. 1 1 2 2 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. for Example 4 GUIDED PRACTICE

  15. 6. What is the approximate length of AB, with endpoints A(–3, 2) and B(1, –4)? ANSWER B 6.1 units 7.2 units 8.5 units 10.0 units for Example 4 GUIDED PRACTICE

  16. 1. AB bisectsCD at E. IfCE =in., FindCD. in. ANSWER 1 1 2. Point M is the midpoint of XY. Find XM. 4 2 2 4 17 ANSWER Daily Homework Quiz

  17. 3. PointMis the midpoint ofPQwith endpointsP(2, – 6 ) and Q(– 8, 0). Find the coordinates ofM. ANSWER (–3, –3) 4. The midpoint ofGHis M(4, –1). One endpoint isG(5, 3) . Find the coordinates ofH. ANSWER (3, –5) Daily Homework Quiz

  18. 11.7 ANSWER Daily Homework Quiz 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.

  19. 1.3 Use midpoint and distance formulas You will find lengths of segments in the coordinate plane Essential question: How do you find the distance and the midpoint between two points in the coordinate plane? The midpoint of a segment is the point that divides the segment into two congruent parts. The length of a segment in the coordinate plane is the distance between its endpoints. To find the distance between the points (a,b) and (c,d) use the distance formula d= (d-b)2+(c-a)2. To find the midpoint, use the midpoint formula (a+c, b+d) 2 2

More Related