Lesson 7. Understanding the Distance Formula Solve. Show our work. Round our answers to the nearest tenth if necessar.. Points P (, ) and Q (, ) are plotted on a coordinate plane. Find the eact distance between points P and Q. P (, ) 0 5 Q (, ). Find the distance between each pair of points. Which pair of points are the least distance apart? a) A (, ), B (0, ) b) C (, ), D (, 6) c) E (, ), F (7, 8) d) G (, ), H (, 5). Samantha plots the points P (, ), Q (, ), and R (, ) on a coordinate plane. She joins the three points to form triangle PQR. Is the triangle a right triangle? Eplain. P (, ) 0 Q (, ) R (, ) Etra Practice Course B 9
Use the data in the diagram for Questions to 6. Each unit on the grid equals kilometer. Bank (5, ) Home (, ) Post Office (, ) 5 0 5 Cinema (, ) School (, ). Find the approimate distance from Mar s home to each of the following locations. a) Bank b) Cinema c) Post Office d) School 5. Which three locations are the same distance from Mar s home? 6. On a particular da, Mar traveled from her home to school. After school, she went to the post office to mail a letter. Then, she went home. Find the total distance she traveled. 0 Chapter 7 Lesson 7.
Solve. Show our work. 7. Town A and town B are located at the points shown in the diagram. Mr. Appleton wants to drive from town A to town B. He can choose between the route that takes him through towns P and Q, or the route that takes him through town R. Each unit on the grid equals kilometer. Town R (, ) 5 Town A (, ) Town B (, ) 0 Town Q (0, ) Town P (, ) a) Which is the shorter route? b) What is the difference in distances of the two routes? Etra Practice Course B
Solve. Show our work. Round our answer to the nearest tenth. 8. The positions of a boat and a lighthouse are shown on the grids. Each unit on the grid equals mile. Boat (, ) 0 Lighthouse (, ) 5 a) How far is the boat from the lighthouse? b) The boat takes 0 minutes to travel to the lighthouse. Find the speed of the boat in miles per hour. Chapter 7 Lesson 7.
c) Area of shaded triangle:? PR? SU 5 975? 0.? SU 975 5.55 SU 975 5.55 5.55 SU 8.9 ft The length of SU is approimatel 8.9 feet.. a) Let the distance between town A and town C on the map be centimeters. 5 6 7 5 6 9 5 85 Let the distance between town A and town D on the map be centimeters. 5 8 85 5 6 85 6 5 6 6 5 5. In ABD, 5.58 cm Let the actual distance between town A and town D be d kilometers. Map scale: : 50,000 50,000 cm 5 0.5 km.58 0.5 d.58 0.5 0.5 0.5 d.9 d.9 d d d d. km The actual distance between town A and town D is approimatel. kilometers. AB AD 5? BD 0 6 5? 5 656 65 So, triangle ABD is not a right triangle. In BCD, BD CD 5? BC 5 60 5? 65,5 5,5 So, triangle BCD is a right triangle. Lesson 7.. Plot a point X(, ) to form the third verte of a right triangle. PX ( ) 6 units QX ( ) 8 units PX QX 5 PQ 6 8 5 PQ 6 6 5 PQ 00 5 PQ PQ 00 PQ 5 0 The eact distance between points P and Q is 0 units.. a) Distance from A to B 0 9.6 units b) Distance from C to D 6 8 6 68 8. units c) Distance from E to F ( ) ( ) 7 8 0 00.9 units d) Distance from G to H 5. units Points G and H are closest to each other. Etra Practice Course B 6
. Distance from P to Q 6 7 units Distance from Q to R 6 7units Distance from P to R 9 9 98 units The longest side is PR. PQ QR 5? PR ( 7) ( 7) 5? ( 98) 7 98 So, triangle PQR is not a right triangle.. a) Distance from Mar s home to the bank 5 ( ) 6 6 0 6. km The bank is approimatel 6. kilometers from Mar s home. b) Distance from Mar s home to the cinema 6 6 0 6. km The cinema is approimatel 6. kilometers from Mar s home. c) Distance from Mar s home to the post office 9 0. km The post office is approimatel. kilometers from Mar s home. d) Distance from Mar s home to the school ( ) ( ) 6 6 0 6. km The school is approimatel 6. kilometers from Mar s home. 5. The bank, the cinema, and the school are the same distance from Mar s home. 6. Distance from school to the post office ( ) ( ) 9 50 7. km Total distance traveled 6. 7.. 5 6.6 km The total distance Mar traveled was 6.6 kilometers. 6 Answers
7. a) AP 5km PQ 0 99 8 km QB 5 km Route via P and Q 5 8 0.8 km AR 5 6 km RB 6 7 km Route via R 6 7.8 km The shorter route is the route that takes him through towns P and Q. b) Difference between the two routes.8 0.8 5 0.7 km The difference in the distances of the two routes is 0.7 kilometers. 8. a) Distance from boat to lighthouse RB 5 7 5 9 7 units Actual distance from boat to lighthouse 7. mi The boat is approimatel. miles from the lighthouse. b) 0 min 5 h Distance 5 Speed Time. Speed. 5 Speed Speed 5.9 mi/h The speed of the boat is.9 miles per hour. Lesson 7.. a 5 5 a 5 5 a 5 69 a 69 a 5. b 5 b 576 65 b 576 576 65 576 b 9 b 9 b 7 b 5 7 b 5. Diameter of clinder 5 5 5 0 cm 5 0 0 5 900 00 5,000, 000.6. Radius of sphere. 5 0.6 m 5 0.6 0.6 5 0.6 0.6 5 0.7 0.7 0.8 Etra Practice Course B 6