Geometry with Data Analysis PDF Practice Questions

3.5 Start Thinking In a coordinate plane, graph the lines y = x − 3 and y = x + 2. Do the lines intersect? If so, at what point? Graph the line y = − x + 5 in the same coordinate plane. At what points does this line intersect y = x − 3 and y = x + 2? How can you describe the angles created b...

3.5 Start Thinking In a coordinate plane, graph the lines y = x − 3 and y = x + 2. Do the lines intersect? If so, at what point? Graph the line y = − x + 5 in the same coordinate plane. At what points does this line intersect y = x − 3 and y = x + 2? How can you describe the angles created by the intersections? 3.5 Warm Up Graph the line in a coordinate plane. 1. y = 6 x 2. y = 4 x + 2 3. y = x − 3 4. y = x + 2 5. y = 2x −2 6. y = − 43 x + 3 3 3.5 Cumulative Review Warm Up Name the property of equality the statement illustrates. 1. If x = y, then 2 x = 2 y. 2. If BN = NC , then BN − 6 = NC − 6. 3. z = z 4. m∠A = m∠A 5. If m∠D = 38° and m∠E = 38°, then m∠E = m∠D. 6. If FG = JK , then JK = FG. 98 Geometry with Data Analysis Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved. Name_________________________________________________________ Date __________ 3.5 Practice A In Exercises 1 and 2, use the graph to identify two solutions of the linear equation. Check your answers. 1. 2. In Exercises 3 and 4, tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer. 3. Line 1: ( 2, 3), ( 4, 12) 4. Line 1: ( − 6, −10), ( 4, − 2) Line 2: (5, 10), (14, 8) Line 2: ( − 8, − 6), (0, 4) In Exercises 5 and 6, write an equation of the line passing through point P that is parallel to the given line. 5. P ( −1, 3), y = 4 x − 7 6. P ( 2, − 3), y = − 6 x + 10 In Exercises 7 and 8, write an equation of the line passing through point P that is perpendicular to the given line. 7. P (6, 10), y = − 3 x + 13 8. P (0, − 8), y = − 1 x − 10 3 In Exercises 9 and 10, find the distance from point Q to the given line. 9. Q ( 2, 6), y = − x + 4 10. Q ( −10, − 4), 5 x − y = 6 11. A line through (3, 5) and ( k , 12) is perpendicular to a line through (0, 7) and (2, 10). Find the value of k that makes the above statement true. 12. Your friend claims that if a line has a slope that is less than 1, then any line perpendicular to it must have a positive slope. Is your friend correct? Explain your reasoning. 13. You draw a coordinate plane on a map. Each grid line represents 100 meters. You are located at the point ( 2, 6) and a path is represented by y = 2 x − 9. How far are you from the path? Copyright © Big Ideas Learning, LLC Geometry with Data Analysis 99 All rights reserved. Resources by Chapter Name _________________________________________________________ Date _________ 3.5 Practice B In Exercises 1 and 2, use the graph to identify two solutions of the linear equation. Check your answers. 1. 2. 3. Tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer. Line 1: ( 2.5, − 2), (9.5, 12) Line 2: ( − 4, − 2), (8, − 4) 4. Write an equation of the line passing through point P( −1, − 4) that is parallel to y = − 6 x + 8. 5. Write an equation of the line passing through point P ( −1, 3) that is perpendicular to y = 4 x − 7. In Exercises 6 and 7, find the distance from point P to the given line. 6. P ( 4, 8), 6 = y + 2 x 7. P ( − 2, 1), y = 1 x − 3 4 8. A line through ( −1, b) and (c, 8) is parallel to a line through ( − 6, 3) and (0, 12). Find values of b and c that make the above statement true. 9. The graph shows three lines. The slope of line 1 is m1, where −1 ≤ m1 < 0. a. Lines 1 and  2 are parallel. What do you know about the y 3 slope of line  2 ? 3 b. Lines 1 and  3 are perpendicular. What do you know about 1 1 the slope of line  3 ? −2 2 4 x c. What is the relationship between  2 and  3 ? 2 −3 Justify your answer. 10. Two lines are perpendicular. Is it possible for the lines to have the same y-intercept? Justify your answer. 11. You draw a coordinate plane on a map. Each grid line represents 10 feet. You are located at ( − 4, − 3). A stream is represented by y = − 1 x. A trail is represented 2 1 by y = x − 3. You walk directly to the stream, and then directly from the 2 stream to the trail. How far do you walk? 100 Geometry with Data Analysis Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved. Name_________________________________________________________ Date __________ 3.5 Enrichment and Extension Equations of Parallel and Perpendicular Lines 1. Write the equation of the perpendicular bisector for the line segment defined between points A( 2, 5) and B( − 6, −1). 2. Find the values of a and b in ax + by = 90 such that the equation is perpendicular to − 20 x + 12 y = 36 and has the same y-intercept. 3. Consider the linear equation y = 3.62( x − 1.35) + 2.74. a. What is the slope of this line? b. What is the value of y when x = 1.35? c. Find an equation for the line through ( 4.23, − 2.58) that is parallel to this line. d. Find an equation for the line through ( 4.23, − 2.58) that is perpendicular to this line. 4. What is the slope of the line ax + by = c? Find an equation for the line through the origin that is parallel to the line ax + by = c. Find an equation for the line through the origin that is perpendicular to the line ax + by = c. 5. A line passes through the points ( k + 10, − 2k − 1) and ( 2, 9) and has a y-intercept of 10. Find the value of k and the equation of the line. 6. A line passes through the points (3k , 6k − 5) and ( −1, − 7) and has a y-intercept of − 5. Find the value of k and the equation of the line. 7. Consider the two linear equations ax + by = c and dx + ey = f. a. Under what conditions will the graphs of the two equations intersect at one point? b. Under what conditions will the graphs of the two equations be parallel? 8. Point F is located at (0, 4). a. Find coordinates of three points that are equidistant from F and the x-axis. b. If possible, write the equations of the lines that are parallel or perpendicular to the line x = 0 and pass through the coordinates from part (a). c. Consider G (0, y ). Find the coordinates of three points that are equidistant from G and the x-axis. Copyright © Big Ideas Learning, LLC Geometry with Data Analysis 101 All rights reserved. Resources by Chapter Name _________________________________________________________ Date _________ 3.5 Puzzle Time How Do You Make Seven Even? Circle the letter of each correct answer in the boxes below. The circled letters will spell out the answer to the riddle. Complete the sentence. 1. The perpendicular bisector of AB is a line that is perpendicular to AB and passes through the ____________ of AB. 2. In a coordinate plane, two nonvertical lines are parallel if and only if they have the ____________. 3. In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their ____________. Tell whether the lines through the given points are (1) parallel, (2) perpendicular, or (3) neither. 4. Line 1: ( − 7, − 3), (1, 4) ; Line 2: ( − 6, 6), (1, − 2) 5. Line 1: ( − 4, − 2), ( 4, 5) ; Line 2: ( − 2, 3), ( 2, − 3) 6. Line 1: (0, 4), ( − 6, 0); Line 2: (3, 2), ( − 3, − 2) Find the distance from point A to the given line. Round to the nearest tenth. 7. A( − 4, 4), y = 0.8 x − 0.4 8. A( − 3, − 3), y = 0.5 x + 6.5 R D N R P O M A 5 2 6.4 slopes is −1 slopes is − 1 5.9 straight 5.3 2 P T L H L I E S 7.2 1 6.7 same slope slopes is 0 4 midpoint 3 102 Geometry with Data Analysis Copyright © Big Ideas Learning, LLC Resources by Chapter All rights reserved.