Question

The library is at point (1,1). The gym is at point (1,-4). The chemistry lab is at point (-3,6). The restrooms are at point (-3,1). The teacher's lounge is at point (4,6). The principal's office is at point (-5,-4). The auditorium is at point (4,-2). And the physics lab is at point (-1,-2). Which of these pairs of places lie 4 units from one another?

Answer 1

Answer: Library and Restrooms

Step-by-step explanation: got it right on Study Island

Answer 2

Library and restrooms are only the places which lie 4 units from each another.

Explanation:

Given that the library is at point (1,1). The gym is at point (1,-4). The chemistry lab is at point (-3,6). The restrooms are at point (-3,1). The teacher's lounge is at point (4,6). The principal's office is at point (-5,-4). The auditorium is at point (4,-2). And the physics lab is at point (-1,-2).

These points are labelled on the graph as shown in attachment.

Now, the points which are nearer we can calculate the distance by distance formula which is written as
`s=\sqrt{(x_(2)-x_(1))  ^(2)+(y_(2)-y_(1))  ^(2) }`

Now, distance between the points (-3, 1) and (1,1)

`s=\sqrt{(1+3)^(2)+(1-1)^(2) }` ⇒ s=4 units

Now, the distance between the points (-1,-2) and (-5, -4)

`s=\sqrt{(-5+1)^(2)+(-4+2)^(2) }` ⇒ s=
`\sqrt 20units`

Now, the distance between the points (4,-2) and (1, -4)

`s=\sqrt{(1-4)^(2)+(-4+2)^(2) }` ⇒ s=
`\sqrt 13units`

Now, the distance between the points (-3,1) and (-1,-2)

`s=\sqrt{(-1+3)^(2)+(-2-1)^(2) }` ⇒ s=
`\sqrt 13units`

Similarly, by calculating only 1 pair lie 4 unit from one place to another.

Library and restrooms are only the places which lie 4 units from each another.