On a map where each unit represents 100 miles, two airports are located at P(1,17) and Q(12,10). What is the distance, to the nearest whole mile, between the two airports?
A.
1,800 miles
B.
1,304 miles
C.
1,122 miles
D.
900 miles
The distance formula, $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ can be used here. This means the distance is $\sqrt{(12-1)^2 + (10-17)^2} = \sqrt{11^2 + (-7)^2} = \sqrt{170} \approx \sqrt{169} = 13$. Therefore, the distance is $\boxed{\text{(B)}\ 1,304\ \text{miles}}$.
To find the distance between two points on a map, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points on the map.
In this case, the coordinates of the two airports are P(1,17) and Q(12,10).
Plugging in the coordinates into the formula:
d = sqrt((12 - 1)^2 + (10 - 17)^2) = sqrt(11^2 + (-7)^2) = sqrt(121 + 49) = sqrt(170) ≈ 13.038
Now, since each unit on the map represents 100 miles, we need to multiply the result by 100 to get the actual distance in miles:
13.038 * 100 ≈ 1,304
So, the nearest whole mile distance between the two airports is approximately 1,304 miles.
Therefore, the correct answer is B. 1,304 miles.
To find the distance between two points on a map, we'll use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Given the coordinates of airport P as (1, 17) and airport Q as (12, 10), we can substitute these values into the formula:
d = √((12 - 1)^2 + (10 - 17)^2)
Simplifying:
d = √(11^2 + (-7)^2)
d = √(121 + 49)
d = √(170)
d ≈ 13.038 miles
Rounding to the nearest whole number, the distance between the two airports is approximately 13 miles.
So the answer is B. 13 miles.