Parallel and perpendicular lines: Homework Problems

Transcription

1 October 16, 2013 Parallel and perpendicular lines page 1 Parallel and perpendicular lines: Homework Problems Notes for Review: For parallel lines and for perpendicular lines, there are special relationships between slopes. If two lines are parallel, they have equal slopes. 4 3 If two lines are perpendicular, they have opposite reciprocal slopes (example: 3 and ). 4 (An exception: You can t use the above rules when vertical lines are involved, because vertical lines don t have slopes. But for vertical lines, the only parallel lines are other vertical lines, and the only perpendicular lines are horizontal lines.) 1. For each pair of lines described below, are the lines parallel, perpendicular, or neither? a. Line #1 goes through ( 1,7) and ( 6, 8); line #2 goes through ( 4, 13) and (3,8). b. Line #1 goes through (2,4) and (7,14); line #2 goes through ( 2,8) and (4,5). c. Line #1 goes through ( 1,2) and ( 1, 8); line #2 goes through (5, 2) and (11, 2).

2 October 16, 2013 Parallel and perpendicular lines page 2 2. The four lines shown on the grid form a rectangle. a. What do you know about the slopes of opposite sides of a rectangle? b. What do you know about the slopes of adjacent sides of a rectangle? c. How many slopes would you need to find from the graph, after which all the other slopes of the rectangle will be known? d. Write equations for the four lines that form the rectangle. 3. Given the equation y = 1.25x + 4, write equations for three other lines so that the four lines form a rectangle.

3 October 16, 2013 Parallel and perpendicular lines page 3 Here s an example of an important type of problem involving perpendicular lines. Example: Find an equation for a line that is perpendicular to y = 35 x + 2 and that passes through the point ( 1, 4). Solution: Since a point is given, point-slope form is an excellent choice for this problem. 3 The given line has a slope of 35, so the requested line has the opposite reciprocal slope:. 5 3 Now write the answer using point-slope form: y = (x + 1) = 4. 5 You can do the same kind of thing with parallel lines. The only change is: use the same slope instead of an opposite-reciprocal slope. Problems 4. For both parts of this problem, the given line is: y = 3x 7. a. Write an equation for a line that is parallel to the given line, and passes through (2, 5). b. Write an equation for a line that is perpendicular to the given line, and passes through (2, 5). 5. Let L stand for the line that passes through points (5, 1) and ( 3, 7). a. Write an equation for line L. b. Write an equation for a line that is parallel to L and passes through the point (2, 0). c. Write an equation for a line that is perpendicular to L at the point (5, 1).

4 October 16, 2013 Parallel and perpendicular lines page 4 6. a. Write equations for two lines that intersect each other perpendicularly on the y-axis at (0, 4). Hint: Easier in slope-intercept form. b. Write equations for two lines that intersect each other perpendicularly on the x-axis at (4, 0). Hint: Easier in point-slope form. 7. Triangle ABC has its vertices at whole number coordinates as shown in the graph. a. Write equations for lines AB, AC, and BC. AB: AC: BC: b. Write an equation for the triangle s altitude (or height), passing through A and perpendicular to BC. Also draw this line accurately on the grid.

5 October 16, 2013 Parallel and perpendicular lines page 5 Modeling problem 8. Suppose you are heating some water to make it boil. The water temperature increases by 12 degrees each minute. After 5 minutes of heating, the water temperature is 152 degrees. Let T(x) to stand for the water temperature after x minutes of heating. a. Write a function formula equation for the water temperature. All the other questions on this page should be answered by using the part a equation for either evaluating or solving. b. What will the water temperature be after 10 minutes of heating? c. After how many minutes of heating will the water reach the boiling point (212 degrees)? d. Evaluate T(0) and explain the meaning of the answer in terms of the problem situation. e. Solve T(x) = 140 and explain the meaning of the answer in terms of the problem situation.