Question

The endpoints of AB are A(3,-4) and B(11,b). The midpoint of AB is M(n,3). Find Values of b and n?

Answer 1

`n=7color(white)("xxxxxxx")b=10`

Explanation:

In general the midpoint between coordinates `(p_1,q_1)` and `(p_2,q_2)` is `((p_1+p_2)/2,(q_1+q_2)/2)`
That is, the `x` and `y` coordinates of the mid point can be calculated independently from each other.

If `(n,3)` is the midpoint between `(3,-4)` and `(11,b)`
then
`color(white)("XXX")n=(3+11)/2=7`
and
`color(white)("XXX")3=(-4+b)/2color(white)("xx")rarrcolor(white)("xx")3xx2+4=bcolor(white)("xx")rarrcolor(white)("xx")b=10`