Question

Adams house, the local park, and the nearest hospital are mapped on a coordinate plane. what's the distance between Adams house and the hospital?

Answer 1

The distance between two points is given by:

$d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

From the plane we notice that Adam's house is located in the point (-4,2) and the hospital in the point (5,7).

Plugging this values in the formula we get:

$\begin{gathered} d(A,H)=\sqrt[]{(7-2)^2+(5-(-4))^2} \\ =\sqrt[]{(5)^2+(9)^2} \\ =\sqrt[]{25+81} \\ =\sqrt[]{106} \end{gathered}$

Therefore the distance between Adam's house and the hospital is the square root of 106 and the answer is D.