Question

Winston-Salem is halfway between Boone and Raleigh. Burlington is halfway between Winston- Salem and Raleigh. If Boone is located at the coordinates (-1,3) and Raleigh is at (-5, 9), what are the coordinates of Burlington?

Answer 1

The answer is (-4, 15/2)

Explanation:

Let the Boone be x, Winston-Salem be y, Raleigh be z and Burlington be m.

We are given that Winston-Salem is halfway between Boone and Raleigh. Burlington is halfway between Winston- Salem and Raleigh.

If Boone is located at the coordinates (-1,3) and Raleigh is at (-5, 9).

We will use Midpoint Formula

`( (x _(1) + x _(2))/(2) , (y _(1) + y _(2))/(2) ) \\`

Where,

x₁ = (-1) and x₂ = (-5)

y₁ = 3 and y₂ = 9

Now, We will find Co-ordinates of y i.e., Winston-Salem.

So,

`( (( - 1) + ( - 5))/(2) , (3 + 9)/(2) ) \\`

`( (( - 1 - 5))/(2) , (12)/(2) ) \\`

`( ( - 6)/(2) , (12)/(2) ) \\`

`( - 3,6)`

Here, The coordinates of y i.e., Winston-Salem is (-3, 6).

Now, We will find Co-ordinates of m i.e., Burlington.

So,

Again, Using of Midpoint Formula;

Where,

x₁ = (-3) and x₂ = (-5)

y₁ = 6 and y₂ = 9

So,

`( (( - 3) + ( - 5))/(2) , (6 + 9)/(2) ) \\`

`( (( - 3 - 5))/(2) , (15)/(2) ) \\`

`( (( -8))/(2) , (15)/(2) ) \\`

`( - 4 , (15)/(2) ) \\`

Thus, The coordinates of Burlington is (-4, 15/2).