Question

Fraiser drew a model of his hometown on the coordinate plane below. Each unit of the coordinate plane represents 1 mile. A grocery store is located at (6, 4) and a school is located at (6, 8). What is the distance between the grocery store and the school?

Answer 1

The distance between the grocery store and the school is 4 miles.

Explanation:

Given that each point is represented in rectangular form. The staight-line distance (
`d`) between two points on a plane is given by the Pythagorean Theorem:

`d =SF\cdot \sqrt{(x_(B)-x_(A))^(2)+(y_(B)-y_(A))^(2)}`

Where:

`x_(A)`,
`x_(B)` - Horizontal locations of points A and B, dimensionless.

`y_(A)`,
`y_(B)` - Vertical locations of points A and B, dimensionless.

`SF` - Scale factor, measured in miles.

If
`SF = 1\,mi`,
`A = (6, 4)` and
`B = (6,8)`, the straight line distance is:

`d = (1\,mi)\cdot \sqrt{(6-6)^(2)+(8-4)^(2)}`

`d = 4\,mi`

The distance between the grocery store and the school is 4 miles.