Question

The point (2,3/2) is the midpoint of a line segment whose endpoints are (n-2,-6) and (-1,9). Use coordinate geometry to find the numerical value of n

Answer 1

`n=7`

Explanation:

we know that

The formula to calculate the midpoint between two points is equal to

`M=((x_1+x_2)/(2),(y_1+y_2)/(2))`

In this problem we have

`M=(2,(3)/(2))`

`(x_1,y_1)=(n-2,-6)`

`(x_2,y_2)=(-1,9)`

substitute in the formula

`(2,(3)/(2))=((n-2-1)/(2),(-6+9)/(2))`

`(2,(3)/(2))=((n-3)/(2),(3)/(2))`

Equate the x-coordinates both sides

`2=(n-3)/(2)`

Solve for n

Multiply by 2 both sides

`4=n-3`

Adds 3 both sides

`4+3=n`

`n=7`