College Algebra
1.1 Homework – Distance and Midpoint Formulas
Name: _______________________
The distance from Rocky Mountain High School to Steamboat Springs is about 160 miles by car. We approximate it will
take about 3 ½- 4 hours to drive there. A friend has a plane and has offered to fly us there (with their new pilot’s
license), but we’re a little nervous about their lack of experience in the cockpit. A rectangular coordinate system with
coordinates in miles is placed on the map in the figure shown. Steamboat has coordinates (-60, -2) and Rocky Mountain
High School has coordinates (65,1).
a) How long will it take the plane averaging 250 miles per hour to fly directly from Fort Collins to Steamboat? Give
your answer in minutes. Recall: Distance = (Rate) x (Time)
b) Suppose you know the distance in the air from Fort Collins to Walden is 90 miles. You know the y-coordinate of
Walden is 25. We wish to determine the x-coordinate, using the distance formula and solving the algebraic
equation for . State the equation modeling this situation and solve for , round to 2 decimal places. Does your
answer seem reasonable for the map that is shown above?
c) If we fly directly from Fort Collins to Walden, determine the coordinates of the midway point.
d) I would like to find all points on the y-axis that are 80 miles from Steamboat. Write the distance formula for this
scenario and solve for the y-coordinates that meet this requirement. Round to 2 decimals.
e) Find all points having a y-coordinate of −10whose distance from Fort Collins is 20 miles. Round to 2 decimals.
College Algebra
Dog on a Leash
Name: ___________________________________
On a separate piece of paper, solve the following problem. Show all algebra involved in your solution.
1. Write THREE inequalities stating where the dog can roam. Make sure you notice where the origin is so
you can locate the center of each circle. Sketch in the three separate areas.
2. What is the total area the dog can roam? Leave answer in terms of .
3. Write the equation of a line through the points (3, 5) and (6, 9) in slope-intercept form.