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

Calculate the distance between two points on a coordinate plane using the distance formula sqrt((x2 - x1)^2 + (y2 - y1)^2) and convert the distance to real-world measurements if necessary using the map's scale.

Step-by-step explanation:

Finding the Distance between Two Points on a Coordinate Plane

To calculate the distance between Adam's house and the hospital on a coordinate plane, we can use the distance formula derived from the Pythagorean theorem. The distance formula is sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points. If we have the coordinates for Adam's house and the hospital, we would plug them into the formula to find the distance.

As a hypothetical example, if Adam's house is at (3,4) and the hospital is at (6,8), the distance calculated would be sqrt((6-3)^2 + (8-4)^2) = sqrt(3^2 + 4^2) = sqrt(9+16) = sqrt(25) = 5 units.

Remember that this number represents the distance in the units used on the coordinate plane. If the map has a scale, we could then convert these units into a real-world measurement like feet or meters.

Answer 2

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.