Question

The midpoint of the line joining (a,2) and (3,6) is (2,b). Find the values of a and b?

Answer 1

`a=1`
`b=4`

Explanation:

The mid point is actually the mean values.

Given:
Set point 1 as `P_1->(x_1,y_1)=(a,2)`
Set point 2 as `P_2->(x_2,y_2)=(3,6)`

The mean point given as: `P_("mid")->(x_m,y_m)=(2,b)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So the mean `x` value is: `color(white)("d")x_m=(a+3)/2=2`

Multiply both sides by 2 giving:

`a+3=4`

Subtract 3 from both sides

`a=1`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So the mean '`y` value is: `color(white)("d")y_m=b=(2+6)/2=4`