Concept explainers
Halfway Point Two friends live in the city described in Exercise 122, one at the corner of 3rd St. and 7th Ave., the other at the corner of 27th St. and 17th Ave. They frequently meet at a coffee shop halfway between their homes.
- (a) At what intersection is the coffee shop located?
- (b) How far must each of them walk to get to the coffee shop?
122. Distances in a City A city has streets that run north and south and avenues that run east and west, all equally spaced. Streets and avenues are numbered sequentially, as shown in the figure. The walking distance between points A and B is 7 blocks—that is, 3 blocks east and 4 blocks north.
To find the straight-line distance d, we must use the Distance Formula.
- (a) Find the straight-line distance (in blocks) between A and B.
- (b) Find the walking distance and the straight-line distance between the corner of 4th St. and 2nd Ave. and the corner of 11th St. and 26th Ave.
- (c) What must be true about the points P and Q if the walking distance between P and Q equals the straight-line distance between P and Q?
(a)
To find: The intersection point where the coffee shop located.
Answer to Problem 114E
The intersection point where the coffee shop located is 15 St.and 12 Ave.
Explanation of Solution
Given:
Two points where the friends lived are 3St.and 7Ave and 27St.and 17Ave.
Formula used:
The formula to calculate the midpoint of line segment from
Calculation:
In cartesian co-ordinate system the points are in ordered pair. Assume
Substitute
Hence, the intersection point is where the coffee shop located is 15 St and 12 Ave.
(b)
To find: The distance travelled by each friend to get to the coffee shop.
Answer to Problem 114E
The distance travelled by each friend to get to the coffee shop is 20 blocks.
Explanation of Solution
Given:
Two points where the friends lived are 3St.and 7Ave and 27St.and 17Ave and the point of intersection is 15St.and 12Ave.
Calculation:
The walking distance between the first friend house and the coffee shop is 15 blocks east and 5 blocks north.
Hence, the distance travelled by each friend to get to the coffee shop is 20 blocks.
Chapter 1 Solutions
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