Question

If the midpoint of the line segment joining A(x,5) and B(x+1,6) is (3,5) then the value of x is

please find it for me ​

Answer 1

x = 5/2

Explanation:

The midpoint of two points

(x1 , y1) and (x2, y2) is Given by

`M = ( (x1 + x2)/(2) , (y1 + y2)/(2) )`

where M is the midpoint

From the question the midpoint is

( 3 , 5) and the points are

A(x,5) and B(x+1,6)

In order to find x find the midpoint of A and B and compare with the original midpoint

That's

`(3,5) = ( (x + x + 1)/(2) , (5 + 6)/(2 ) )`

`(3,5) = ((2x + 1)/(2) , (11)/(2) )`

Comparing the x coordinate of the midpoint with the x coordinate of the unknown point

That's

`3 = (2x + 1)/(2)`

Cross multiply

6 = 2x + 1

2x = 5

Divide both sides by 2

x = 5/2

Hope this helps you