Calculate the distance between two towns located at coordinates (2, −5) and (3, 7).

Question

ScanSolve AI Tutor · Accepted Answer

To calculate the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ , we use the distance formula:

D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Identify the coordinates of the two towns.
Town X is at $(x_1, y_1) = (2, -5)$ .
Town Y is at $(x_2, y_2) = (3, 7)$ .
Substitute the coordinates into the distance formula.
$D = \sqrt{(3 - 2)^2 + (7 - (-5))^2}$
Calculate the differences in the x and y coordinates.
$D = \sqrt{(1)^2 + (7 + 5)^2}$ $D = \sqrt{(1)^2 + (12)^2}$
Square the differences.
$D = \sqrt{1 + 144}$
Add the squared values.
$D = \sqrt{145}$
Calculate the square root.
$D \approx 12.04159$
The distance between the two towns is approximately 12.04 units.
$\sqrt{145} \text{ units} \approx 12.04 \text{ units}$

Calculate the distance between two towns located at coordinates (2, -5) and (3, 7).