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

Answer:

The answer is (-4, 15/2)

Step-by-step 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

$( \frac{x _{1} + x _{2}}{2} , \frac{y _{1} + y _{2}}{2} )$

Where,

x₁ = (-1) and x₂ = (-5)

y₁ = 3 and y₂ = 9

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

So,

$( \frac{( - 1) + ( - 5)}{2} , \frac{3 + 9}{2} )$

$( \frac{( - 1 - 5)}{2} , \frac{12}{2} )$

$( \frac{ - 6}{2} , \frac{12}{2} )$

$( - 3,6)$

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,

$( \frac{( - 3) + ( - 5)}{2} , \frac{6 + 9}{2} )$

$( \frac{( - 3 - 5)}{2} , \frac{15}{2} )$

$( \frac{( -8)}{2} , \frac{15}{2} )$

$( - 4 , \frac{15}{2} )$

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