Question

A few locations in the town of Shady Brook are mapped out on the coordinate plane below. Each unit on the grid represents one mile.

Part A: Which two locations shown have the same x-coordinate or y-coordinate? Which coordinates do they share?

Part B: How can the shared coordinate from Part A be used to find the distance between the two locations?

Answer 1

Part A: High School (
`-6,6`) and Park (
`2,6`) in Shady Brook share the same y-coordinate. Part B: The distance between them is determined by the difference in their x-coordinates, resulting in a distance of
`8` miles.

Part A: The two locations that have the same y-coordinate are High School (
`-6,6`) and Park (
`2,6`).

Part B: The shared coordinate from Part A (which is the y-coordinate, in this case) can be used to find the distance between the two locations.

The distance between two points with shared y-coordinates is the absolute difference between their x-coordinates.

In this case, the distance between High School (
`-6,6`) and Park (
`2,6`) is |(
`-6`) -
`2`| =
`8` miles.

Answer 2

Part A : High school (-6,6) and Park (2,6) are the two locations which share same y-coordinate.

Part B : the distance between two locations having shared coordinate is difference between the dissimilar (unlike) coordinate.

Explanation:

Part A:

Given, that A few locations in the town of Shady Brook are mapped out on the coordinate plane A few locations in the town of Shady Brook are mapped out on the coordinate plane

And each unit on grid represents one mile.

When you observe the figure,

both High school and park are 6 miles away from X-axis.

so, High school (-6,6) and Park (2,6) are the two locations which share same y-coordinate.

Part B:

so, distance between two points (p,q) , (r,s) is

`\sqrt{(p-r )^(2) +(q-s)^(2) }`

If suppose p=r, then distance between points is just |q-s|.

⇒ distance between points having shared coordinate is just the difference between unlike coordinate of the points.

here, distance between high school (-6,6) and park (2,6) is 2-(-6) = 8.