Question

Find the value of x so that (-2, 4) is the midpoint between (x, 2) and (-5,3).

Answer 1

`\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{x}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{-5+x}{2}~~,~~\cfrac{3+2}{2} \right)~~=~~\stackrel{midpoint}{(-2,4)}\implies \begin{cases} \cfrac{-5+x}{2}=-2\\[1em] -5+x=-4\\ \boxed{x=1} \end{cases}`

Answer 2

The value of x is 1.

Explanation:

Mid point formula : On line connecting to points
`(x_1,y_1)(x_2,y_2)` point (x.y) lies on the mid of line.

`x=(x_1+x_2)/(2)`

`y=(y_1+y_2)/(2)`

We have

`(x_1,y_1)(x_2,y_2)=(x,2)(-5,3)`

Mid point = (-2,4)

`-2=(x+(-5))/(2)`

`-4=x-5`

`x=-4+5=1`

The value of x is 1.