WarmUp 1 Exercises EXAMPLE Find segment lengths Skateboard

Warm-Up 1 Exercises EXAMPLE Find segment lengths Skateboard In the skateboard design, VW bisects XY at point T, and XT = 39. 9 cm. Find XY. SOLUTION Point T is the midpoint of XY. So, XT = TY = 39. 9 cm. XY = XT + TY Segment Addition Postulate = 39. 9 + 39. 9 Substitute. Add. = 79. 8 cm

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

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

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 In Exercises 1 and 2, identify the segment bisector of PQ. Then find PQ. 1. ANSWER 3 MN; 3 4

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 In Exercises 1 and 2, identify the segment bisector of PQ. Then find PQ. 2. ANSWER 5 line l ; 11 7

Warm-Up 3 Exercises EXAMPLE Use the Midpoint Formula a. FIND MIDPOINT The endpoints of RS are R(1, – 3) and S(4, 2). Find the coordinates of the midpoint M.

Warm-Up 3 Exercises EXAMPLE Use the Midpoint Formula SOLUTION a. FIND MIDPOINT Use the Midpoint Formula. M 1 + 4, – 3 + 2 2 2 ANSWER = M 52 , – 21 The coordinates of the midpoint M are 5 – 1 , 2 2

Warm-Up 3 Exercises EXAMPLE Use the Midpoint Formula b. FIND ENDPOINT The midpoint of JK is M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K.

Warm-Up 3 Exercises EXAMPLE Use the Midpoint Formula SOLUTION FIND ENDPOINT Let (x, y) be the coordinates of endpoint K. Use the Midpoint Formula. STEP 1 Find x. 1+ x = 2 2 1+x=4 x=3 ANSWER STEP 2 Find y. 4+ y 1 = 2 4+y=2 y=– 2 The coordinates of endpoint K are (3, – 2).

Warm-Up Exercises GUIDED PRACTICE 3. The endpoints of AB are A(1, 2) and B(7, 8). Find the coordinates of the midpoint M. ANSWER 4. for Example 3 (4, 5) The midpoint of VW is M(– 1, – 2). One endpoint is W(4, 4). Find the coordinates of endpoint V. ANSWER (– 6, – 8)

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

Warm-Up 4 Exercises EXAMPLE Standardized Test Practice RS = 2 2 (x 2– x 1) + (y 2 – y 1) Distance Formula = [(4 – 2)] 2+ [(– 1) – 3] 2 Substitute. = (2) + (– 4 ) 2 = 4+16 = 20 ~ 4. 47 = 2 Subtract. Evaluate powers. Add. Use a calculator to approximate the square root. ANSWER The correct answer is C.

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

Warm-Up Exercises GUIDED PRACTICE 6. for Example 4 What is the approximate length of AB , with endpoints A(– 3, 2) and B(1, – 4)? 6. 1 units ANSWER B 7. 2 units 8. 5 units 10. 0 units

Daily Homework Quiz Warm-Up Exercises 1. AB bisects CD at E. If CE = 2 ANSWER 2. 1 in. , Find CD. 4 4 1 in. 2 Point M is the midpoint of XY. Find XM. ANSWER 17