Question

your travel guide contains a grid map of washington d.c., with each unit on the grid representing 0.25 miles. if the white house is located at (-2, -3) and the smithsonian institute is located at (4, -6), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in miles? round your answer to two decimal places, if necessary.

Explanation:

Step1: Recall the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ in a coordinate - plane is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(4, - 6)$ and $(x_2,y_2)=(-2,-3)$.

Step2: Calculate the differences in x and y coordinates

$x_2 - x_1=-2 - 4=-6$ and $y_2 - y_1=-3-( - 6)=-3 + 6 = 3$.

Step3: Substitute into the distance formula

$d=\sqrt{(-6)^2+3^2}=\sqrt{36 + 9}=\sqrt{45}\approx6.71$ (in grid units).

Step4: Convert grid units to miles

Since each grid unit represents $0.25$ miles, the distance in miles is $d_{miles}=6.71\times0.25 = 1.68$ miles.

Answer:

$1.68$ miles