MA005 Calculus 1 Coaching Session 1.2.1 # 7

ma005

#1

Hi this is Swapnila! I am a Student Success Coach and will be explaining some practice problems from the MA005 Calculus course. Today we will review an assigned problem from Unit 1. In the “Homework Assessment” you were asked to solve this problem:

The blocks in a city are all perfect squares. A friend gives you the following directions to a good restaurant;
"go north 3 blocks, turn east and go 5 blocks, turn south and go 7 blocks, turn west and go 3 blocks."
How far away (straight line distance) is the restaurant?

To find how far away is the restaurant, use the distance formula. Our approach for this problem will be as follows:
1.Draw the figure by using the given information.
2.Find out the missing distances.
3.Use the appropriate formula or theorem to find the distance.

Step 1: Draw the figure by using the given information:
The figure is as follows:
image

Step 2: Find out the missing distances:
From the above figure, if we extend the bottom line and left line to form a rectangle, we get the rectangle as follows:
image
As this is a rectangle, its opposite sides are same in length.
That is, AE = BC and AB = EC.
AE and EC are the additions of two parts.
That is,
AF + FE = AE = BC and ED + DC = EC = AB
Substitute the known values:
3 + FE = 7 and 5 = ED + 3
Simplify, and solve for unknown terms:
FE = 4 and ED = 2
It means restaurant is at 4 blocks to south and 2 blocks to east.

Step 3: Use the appropriate formula and theorem to find the distance:
The straight line distance of the restaurant means the length of FD. To find FD construct the line FD.
image
Since ∆FED is a right angled triangle, use the Pythagorean theorem to find FD:
Pythagorean theorem:
image
Substitute the values of FE and ED:
image
Simplify:
image
image
Switch the sides:
image
Taking square root on both sides:
image
Since distance is always non-negative,
image

Therefore, the restaurant is 4.47 blocks away.

Conclusion: By using the Pythagorean theorem, it is found that the restaurant is 4.47 blocks far away.

In addition to this, I am also attaching the pdf document of the practice problem for your ready reference.
Question 7.pdf (236.0 KB)

Please let me know if you have any question on this problem, or on this topic generally. I will be here in the forum for the next hour.