Lesson 7.2 Understanding the Distance Formula

Transcription

1 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

2 Use the data in the diagram for Questions to 6. Each unit on the grid equals kilometer. Bank (5, ) Home (, ) Post Office (, ) 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.

3 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

4 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.

5 c) Area of shaded triangle:? PR? SU 5 975? 0.? SU SU 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 Let the distance between town A and town D on the map be centimeters 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 km d 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? So, triangle ABD is not a right triangle. In BCD, BD CD 5? BC ? 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 PQ 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 units b) Distance from C to D units c) Distance from E to F ( ) ( ) units d) Distance from G to H 5. units Points G and H are closest to each other. Etra Practice Course B 6

6 . Distance from P to Q 6 7 units Distance from Q to R 6 7units Distance from P to R 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 ( ) km The bank is approimatel 6. kilometers from Mar s home. b) Distance from Mar s home to the cinema 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 ( ) ( ) 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 ( ) ( ) km Total distance traveled km The total distance Mar traveled was 6.6 kilometers. 6 Answers

7 7. a) AP 5km PQ km QB 5 km Route via P and Q km AR 5 6 km RB 6 7 km Route via R km The shorter route is the route that takes him through towns P and Q. b) Difference between the two routes km The difference in the distances of the two routes is 0.7 kilometers. 8. a) Distance from boat to lighthouse RB 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 b b 9 b 9 b 7 b 5 7 b 5. Diameter of clinder cm ,000, Radius of sphere m Etra Practice Course B 6