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Skateboard Design: Segment Lengths and Midpoints

Learn how to find segment lengths and midpoints in a skateboard design using algebraic equations and the midpoint formula.

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Skateboard Design: Segment Lengths and Midpoints

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  1. Sample:(2, 5) ANSWER –3 ANSWER 1.Find a point betweenA(–3, 5) andB(7, 5). 2.Find the average of –11 and 5.

  2. x + 7 3.Solve = 5. 2 3 ANSWER 4.Find√30 to the nearest hundredth. 5.48 ANSWER

  3. 5. Find √5 + √20to the nearest hundredth. 6.71 ANSWER

  4. 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.

  5. 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.

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

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

  15. 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.

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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.

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