Answer:
[tex]n=7[/tex]
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
In this problem we have
[tex]M=(2,\frac{3}{2})[/tex]
[tex](x_1,y_1)=(n-2,-6)[/tex]
[tex](x_2,y_2)=(-1,9)[/tex]
substitute in the formula
[tex](2,\frac{3}{2})=(\frac{n-2-1}{2},\frac{-6+9}{2})[/tex]
[tex](2,\frac{3}{2})=(\frac{n-3}{2},\frac{3}{2})[/tex]
Equate the x-coordinates both sides
[tex]2=\frac{n-3}{2}[/tex]
Solve for n
Multiply by 2 both sides
[tex]4=n-3[/tex]
Adds 3 both sides
[tex]4+3=n[/tex]
[tex]n=7[/tex]
