Questions: On a map, the coordinates for San Antonio are (-7,1) and those for San Diego are (18,11), specified in inches. Find the distance between the cities (on the map) to the nearest tenth of an inch.

Solution Steps

To find the distance between two points on a coordinate plane, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is given by:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Here, \((x_1, y_1)\) are the coordinates of San Antonio and \((x_2, y_2)\) are the coordinates of San Diego. We will plug in the given coordinates into this formula and compute the distance.

The coordinates for San Antonio are \((-7, 1)\) and those for San Diego are \((18, 11)\).

To find the distance between the two points, we use the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the given coordinates: \[ \text{Distance} = \sqrt{(18 - (-7))^2 + (11 - 1)^2} \]

Simplify the terms inside the square root: \[ \text{Distance} = \sqrt{(18 + 7)^2 + (11 - 1)^2} \] \[ \text{Distance} = \sqrt{25^2 + 10^2} \] \[ \text{Distance} = \sqrt{625 + 100} \] \[ \text{Distance} = \sqrt{725} \]

Calculate the square root of 725: \[ \text{Distance} \approx 26.9258 \]

Round the distance to the nearest tenth: \[ \text{Distance} \approx 26.9 \]

Final Answer