Question

a delivery driver needs to calculate the shortest distance between two warehouses located at (3, 4) and (7, 9) on a city map. what is the distance between the warehouses? a. 10 b. \\( \sqrt { 26 } \\) c. \\( \sqrt { 41 } \\) d. 4.5

Explanation:

Step1: Identify the coordinates

Let $(x_1,y_1)=(3,4)$ and $(x_2,y_2)=(7,9)$.

Step2: Use the distance formula

The distance formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Substitute the values: $d=\sqrt{(7 - 3)^2+(9 - 4)^2}$.

Step3: Calculate the differences

$7-3 = 4$ and $9 - 4=5$.
So, $d=\sqrt{4^2+5^2}$.

Step4: Compute the squares

$4^2 = 16$ and $5^2=25$.
Then $d=\sqrt{16 + 25}$.

Step5: Sum and take the square root

$16+25=41$.
So, $d=\sqrt{41}$.

Answer:

C. $\sqrt{41}$