Question

F the endpoints AB of have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of AB?

(5, 3)
(4, 5)
(5, 5)
(4, 3)

Answer 1

In these kind of problems, it's always the best to just draw it. There are "formulas" to calculate this, but it's better to know intuitively.


Midpoint, as the name suggests is the point that is exactly halfway between two points. To find a midpoint in one dimension, we would take an average between those two points.
Example: Number exactly halfway between 8 and 16 is
`(8 + 16)/(2)= 12`

We can do the same for two dimensions, it just means we'll have to calculate both for x-values and y-values

Midpoint
`( (x_(1)+x_(2) )/(2) , (y_(1)+y_(2) )/(2) ) = ( (9-1 )/(2) , (8-2 )/(2) ) =( 4, 3 )`