Question

A park is represented on a map with the following vertices coordinates: Vertex 1 is at (−4, −1) . Vertex 2 is at ​ (−4, 5) ​. Vertex 3 is at (2, 5) . Vertex 4 is at (2, −1) . Linsey jogs along the the edge of the park in order from vertex 1 to vertex 2 to vertex 3 to vertex 4 and then back to vertex 1. One unit on the coordinate grid equals 20 yd. What is the total distance Lindsey jogged? Enter your answer in the box.

Answer 1

check the picture below.

you can pretty much count the units off the grid.

keep in mind that is a square, so all sides are of equal length, and recall that each unit off the grid is 20 yards. So simply get the perimeter of the square off the grid, and multiply it by 20.

Answer 2

Lindsey jogged 480 yards.

Explanation:

The distance between two vectors,
`v_(0)` and
`v_(1)`, in which

`v_(0) = (x_(0), y_(0))`

`v_(1) = (x_(1), y_(1))`

Is given, in units on the coordinate grid, by the following formula:

`D = \sqrt{(x_(1) - x_(0))^(2) + (y_(1) - y_(0))^(2)}`

So:

From vertex 1 to vertex 2

From (-4,-1) to (-4,5)

`D = \sqrt{(-4 - (-4))^(2) + (5 - (-1))^(2)} = 6`

From vertex 2 to vertex 3

From (-4,5) to (2,5)

`D = \sqrt{(2 - (-4))^(2) + (5 - (5))^(2)} = 6`

Total distance is 6+6 = 12 units

From vertex 3 to vertex 4

From (2,5) to (2,-1)

`D = \sqrt{(2 - (2))^(2) + (5 - (1))^(2)} = 6`

Total distance is 6+6+6 = 18 units

From vertex 4 to vertex 1

From (2,-1) to (-4,,-1)

`D = \sqrt{(-4 - (2))^(2) + (5 - (1))^(2)} = 6`

Total distance is 6+6+6+6 = 24 units

Each unit on the coordinate grid equals 20 yards.

So Lindsay jogged 24*20 = 480 yards.