Pre-AP Geometry Worksheet 1.3: Midpoint and Distance

Transcription

1 ! Pre-P Geometr Worksheet.3: Midpoint and Distance Name: Date: Period: For problems -4, ou will have two answers. Show all work. a) Find the other endpoint, point, given endpoint and midpoint M b) Find the distance between points &. Leave answers in simplified radical form. ) (, -) M (5, 5) ) (3, ) M (-5, -) 3) (5, 4) M (, -) 4) (-, 3) M (3, -) 5)Which point on the coordinate grid satisfies the conditions of 3 and -? 6) If a crow leaves Marcus and flies 3 miles due north, then turns and flies 4 miles due east, how far is he from Marcus? Pre-P Geometr Worksheet.3

2 ! Use PEMDS = Parentheses, Eponents, Multiplication/Division, dd/subtract to simplif the following. ( ) 7) ) ) 4 + (0 4 6) 0) 3( + 7) 5 Use lgebraic reasoning to solve the following equations. ) 0 = 3 ) 3 8 = + 9 3) = 6 4) 3( 7) = + 4 Pre-P Geometr Worksheet.3

3 ONLINE H O M E W O R K PRCTICE and PPLICTION EXERCISES Scan page for a Virtual Nerd tutorial video. For additional support when completing our homework, go to PearsonTEXS.com. Find the length of each segment... D Use the figure at the right for Eercises 3 and If RS = 5 and ST = 9, then RT =. 4. If ST = 5 and RT = 40, then RS =. 5. ppl Mathematics ()() The numbers labeled on the map of Florida are mile markers. ssume that Route 0 between Quinc and Jacksonville is straight. R 8 C D E S T 3 7 Quinc Monticello Tallahassee Madison 5 83 Live Oak 303 Lake Cit Macclenn 335 Jacksonville Suppose ou drive at an average speed of 55 mi/h. How long will it take to get from Live Oak to Jacksonville? 6. On a number line, is at - and is at 4. What is the coordinate of C, which is 3 of the wa from to? 7. nalze Mathematical Relationships ()(F) is the midpoint of XY. a. Find X. b. Find Y and XY. 8. Suppose point E has a coordinate of 3 on < EG > and EG = 5. What are the possible coordinates of point G? Use the diagram at the right for Eercises 9 and If D = and C = 4-36, find the value of. Then find C and DC. 0. If ED = + 4 and D = 3-8, find ED, D, and E.. Eplain Mathematical Ideas ()(G) Suppose ou know PQ and QR. Can ou use the Segment ddition Postulate to find PR? Eplain.. Use Multiple Representations to Communicate Mathematical Ideas ()(D) Use the diagram at the right. a. What algebraic epression represents GK? b. If GK = 30, what are GH and JK? Determine the coordinate of the midpoint of the segment with the given endpoints. 3. and and 6 5. and X Y E 3 D 4 3 G H J K C 4 Lesson - Measuring Segments

4 ONLINE H O M E W O R K PRCTICE and PPLICTION EXERCISES Scan page for a Virtual Nerd tutorial video. Find the coordinates of the midpoint of HX. For additional support when completing our homework, go to PearsonTEXS.com.. H(0, 0), X(8, 4). H(-, 3), X(7, - ) 3. H(3, 8), X(-6, -6) 4. H(7, 0), X(5, -8) 5. H(-6.3, 5.), X(.8, -) 6. H(5, ), X ( 4, - 4) 7. Eplain Mathematical Ideas ()(G) The endpoints of are ( -, - 3) and (3, ). Point C lies on and is 5 of the wa from to. What are the coordinates of point C? Eplain how ou found our answer. 8. Do ou use the Midpoint Formula or the Distance Formula to find the following? a. Given points K and P, find the distance from K to the midpoint of KP. b. Given point K and the midpoint of KP, find KP. For each graph, find (a) to the nearest tenth and (b) the coordinates of the midpoint of O 6 O 4 8. Create Representations to Communicate Mathematical Ideas ()(E) Graph the points (, ), (6, -), C(8, 7), and D(4, 9). Draw parallelogram CD, and diagonals C and D. a. Find the midpoints of C and D. b. What appears to be true about the diagonals of a parallelogram? ppl Mathematics ()() The units of the subwa map at the right are in miles. Suppose the routes between stations are straight. Find the distance ou would travel between each pair of stations to the nearest tenth of a mile. 3. Oak Station and Jackson Station 4. Central Station and South Station 5. Elm Station and Smphon Station 6. Cedar Station and Cit Plaza Station 7. Maple Station is located 6 mi west and mi north of Cit Plaza. What is the distance between Cedar Station and Maple Station? 3 O 6 North 4 Jackson Central Cedar Smphon Cit Plaza 4 O 4 Elm Oak 4 South 96 Lesson 5- Midpoint and Distance in the Coordinate Plane

5 Find the distance between each pair of points. If necessar, round to the nearest tenth. 8. J(, -), K(, 5) 9. L(0, 4), M(-8, 4) 0. N(-, -), P(-, -3). (0, 3), (0, ). C(, 6), D(- 8, 8) 3. E(6, - ), F(-, 4) 4. Eplain Mathematical Ideas ()(G) n airplane at T(80, 0) needs to fl to both U(0, 60) and V(0, 85). What is the shortest possible distance for the trip? Eplain. Use Representations to Communicate Mathematical Ideas ()(E) For Eercises 5 9, use the map below. Find the distance between the cities to the nearest tenth. 5. ugusta and rookline 6. rookline and Charleston 7. rookline and Davenport 8. Everett and Fairfield 9. List the cities in the order of least to greatest distance from ugusta. The diagram shows with (, ), (, ), C ( +, ), and D ( +, ). 30. re C and D right angles? Justif our answer. 3. re DM and CM congruent? Eplain. 3. Use triangle congruenc to derive the formula for finding the coordinates of the midpoint M of. Davenport Everett 8 4 Charleston rookline ugusta Fairfield C M D O 33. Select Techniques to Solve Problems ()(C) The endpoints of FH are F ( 7, 7) and H (, 3). Point G lies on FH between F and H, such that FG = 3 5 FH. Select a technique (such as estimation or number sense) that will help ou calculate the coordinates of point G, and eplain our selection. What are the coordinates of point G? Use the diagram for Eercises 34 and 35. Points P(, ) and Q(, ) are the endpoints of a hpotenuse of a right triangle. R(, ) Q(, ) 34. Derive a formula for the distance between P and Q. 35. translation of PQ up n units results in ST with endpoints S(, + n) and T (, + n). Derive a formula for finding ST. Eplain our reasoning. How are PQ and ST related? P (, ) O 36. The endpoints of are ( 3, ) and (9, 4). Points D and E lie on, between and. classmate sas that D = 3 and E = 5 6. What are the endpoints of DE? PearsonTEXS.com 97