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

Answer:

The value of x is 1.

Step-by-step 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.

$x=\frac{x_1+x_2}{2}$

$y=\frac{y_1+y_2}{2}$

We have

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

Mid point = (-2,4)

$-2=\frac{x+(-5)}{2}$

$-4=x-5$

$x=-4+5=1$

The value of x is 1.