`NameLESSONDateClassPractice AMidpoint and Distance in the Coordinate Plane1-6Complete the statements. 1. A coordinate plane is a plane that is divided into four regions by a horizontal number line, the 2. The location, or Use the figure for Exercises 3­5. The midpoint of a segment has an x-coordinate that is the average of x1 x2 the x-coordinates of its endpoints ______ . The midpoint of a segment 2 has a y-coordinate that is the average of the y-coordinates of its y1 y2 endpoints ______ . 2 3. Q has coordinates (0, 0). R has coordinates (3, 0). _ Find the midpoint of QR ._, and a vertical number line, the , of a point are given by an ordered pair (x, y)..4. S has coordinates (0, 5. T has coordinates (3,2). Find the midpoint of QS ._2). Find the midpoint of QT .Use the figure for Exercises 6 and 7._6. I is the midpoint of HJ . H has coordinates (0, 0), and I has coordinates ( 1, 2). Sketch these points in the coordinate plane. Study the graph and guess where _ J will be. Draw HJ . 7. Find the coordinates of J by using the Midpoint Formula. Use the figure for Exercises 8­12. Manuel is out for a jog. The thick lines on the grid are jogging paths. He is on his way home and is at D. His home is at E. Each unit on the grid is 1 mile. 8. Name the coordinates of D. 9. Find how many miles Manuel will jog if he goes straight to the x-axis. 10. Find how many miles Manuel will jog if he stays on the jogging paths all the way home. 11. Find how many miles Manuel will jog if he goes straight to the y-axis.Copyright © by Holt, Rinehart and Winston. All rights reserved.43Holt GeometryLESSONPractice AMidpoint and Distance in the Coordinate PlaneLESSONPractice BMidpoint and Distance in the Coordinate Plane1) and U(1, 6) and W(x 5) 2, y 3)1-61-6_Complete the statements. 1. A coordinate plane is a plane that is divided into four regions by a horizontal number line, the 2. The location, orFind the coordinates of the midpoint of each segment. 1. TU with endpoints T(5, ._(3, 23) 2x-axis coordinates, and a vertical number line, they-axis2. VW with endpoints V( 2, , of a point are given by an ordered pair (x, y)._x y 3 __, _____ ( 4, 2)3. Y is the midpoint of XZ. X has coordinates (2, 4), and Y has coordinates (­1, 1). Find the coordinates of Z. Use the figure for Exercises 4­7. 4. Find AB. 5. Find BC. 6. Find CA.Use the figure for Exercises 3­5. The midpoint of a segment has an x-coordinate that is the average of x1 x 2 the x-coordinates of its endpoints ______ . The midpoint of a segment 2 has a y-coordinate that is the average of the y-coordinates of its y1 y2 endpoints ______ . 2 3. Q has coordinates (0, 0). R has coordinates (3, 0). _ Find the midpoint of QR ._26 units 26 units 4 2 units_ _1 1__, 0 2 (0, 1) 1 1__, 1 24. S has coordinates (0, 5. T has coordinates (3,2). Find the midpoint of QS._7. Name a pair of congruent segments. Find the distances.AB and BC2). Find the midpoint of QT .Use the figure for Exercises 6 and 7._6. I is the midpoint of HJ . H has coordinates (0, 0), and I has coordinates ( 1, 2). Sketch these points in the coordinate plane. Study the graph and guess where _ J will be. Draw HJ. 7. Find the coordinates of J by using the Midpoint Formula. Use the figure for Exercises 8­12. Manuel is out for a jog. The thick lines on the grid are jogging paths. He is on his way home and is at D. His home is at E. Each unit on the grid is 1 mile. 8. Name the coordinates of D. 9. Find how many miles Manuel will jog if he goes straight to the x-axis. 10. Find how many miles Manuel will jog if he stays on the jogging paths all the way home. 11. Find how many miles Manuel will jog if he goes straight to the y-axis.Copyright © by Holt, Rinehart and Winston. All rights reserved.8. Use the Distance Formula to find the distance, to the nearest tenth, between K( 7, 4) and L( 2, 0). 9. Use the Pythagorean Theorem to find the distance, to the nearest tenth, between F(9, 5) and G(­2, 2).6.4 units 11.4 units( 2, 4)Use the figure for Exercises 10 and 11. Snooker is a kind of pool or billiards played on a 6-foot-by-12-foot table. The side pockets are halfway down the rails (long sides). 10. Find the distance, to the nearest tenth of a foot, diagonally across the table from corner pocket to corner pocket.13.4 ft ( 1, 3)11. Find the distance, to the nearest tenth of an inch, diagonally across the table from corner pocket to side pocket.3 miles 4 miles 1 mileHolt Geometry101.8 in.43Copyright © by Holt, Rinehart and Winston. All rights reserved.44Holt GeometryLESSONPractice CMidpoint and Distance in the Coordinate PlaneLESSONReview for MasteryMidpoint and Distance in the Coordinate Plane1-61-61. When using the Distance Formula, the answer is the same regardless of which coordinates are designated (x1, y1) and (x 2, y 2). Demonstrate this fact by showing that (x1 x2)22(y1y2)2(x2x1)2(y22y1) .2The midpoint of a line segment separates the segment into two halves. You can use the Midpoint Formula to find the midpoint of the segment with endpoints G(1, 2) and H(7, 6).y(x1x12x2)(y1x22y2 )y122(x22y1y2 y2x 1)2(y2x22y1) since2x1x2 x122x1 x2 y1 y2 M ______, ______ 2 22x1x2y222y1y2y12_____ _____ M 1 7, 2 6 2 2 8 8 __, __ =M 2 27H (7, 6)M (4, 4) G (1, 2)0 7 xM is the midpoint _ of HG .= M(4, 4) Visualize or sketch each situation. Find the answers without calculating. 2. The midpoint of a segment has coordinates (0, 0). One endpoint has coordinates (a, b). Find the coordinates of the other endpoint. 3. An endpoint of a segment has coordinates (0, 0). The midpoint has coordinates (d, e). Find the coordinates of the other endpoint. Use the figure for Exercises 4­7. 4. On the coordinate plane, plot points A( 3, 1), B(1, 3), C(2, _ and _ 1), _ D( 2, 1). Draw AB, AD, DC, _ and BC. Name the shape. 5. If each square on the grid represents one square meter, find the perimeter of ABCD to the nearest tenth of a meter. 6. Find the area of ABCD._Find the coordinates of the midpoint of each segment. 1.y 62.B (4, 5)3 xyS ( 3, 2) 3x 0 3 3( a,b)A ( 2, 5)306T (1,4)(2d, 2e) (1, 5)_( 1, (3, 6) (5, 0.5)1)3. QR with endpoints Q(0, 5) and R(6, 7)_4. JK with endpoints J(1, ­4) and K(9, 3)rectangle 13.4 m 10 m2 11.7 m_Suppose M(3, 1) is the midpoint of CD and C has coordinates (1, 4). You can use the Midpoint Formula to find the coordinates of D. M (3, 1) x1 x2 y1 y2 M ______, ______ 2 2 y-coordinate of D Set the coordinates equal. Replace (x1, y1) with (1, 4). Multiply both sides by 2. Subtract to solve for x2 and y2. 6)._x-coordinate of D 3 3 6 5 x 1 x2 ______ 2 1 x2 ______ 2 1 x2 x27. Draw BD. Find the perimeter of triangle BCD to the nearest tenth of a meter.1 1 2 68. Suki found a treasure map that was laid out on a grid. T had coordinates (3, 12), U had coordinates (7, 2), and V had coordinates (13, 13). Suki read the map's instructions: First, find the midpoint of segment UV, Or the treasure forever lost will be. Label this dreadful midpoint W, Or being well-off will never trouble you. W is in line with and between T and X, X! How clichéd! Can you guess what is next? TX is exactly two times TW, Be sure at X to bring a shovel or two.y1 y2 ______ 2 4 y2 ______ 2 4 y2 y2The coordinates of D are (5,Name the coordinates where Suki found the treasure.(17, 3)5. M( 3, 2) is the midpoint of RS , and R has coordinates (6, 0). What are the coordinates of S?_( 12, 4) (15, 3)Holt Geometry6. M(7, 1) is the midpoint of WX , and X has coordinates ( 1, 5). What are the coordinates of W? Holt GeometryCopyright © by Holt, Rinehart and Winston. All rights reserved.Copyright © by Holt, Rinehart and Winston. All rights reserved.4546Copyright © by Holt, Rinehart and Winston. All rights reserved.69001_072_Go08an_CRF_c01.indd 46Holt Geometry4/11/07 3:35:26 PM`

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