Question

How do you find the midpoint of (5√2, 2√3), and (√2, 2√3)?

Answer 1

See a solution process below:

Explanation:

The formula to find the mid-point of a line segment give the two end points is:

`M = ((color(red)(x_1) + color(blue)(x_2))/2 , (color(red)(y_1) + color(blue)(y_2))/2)`

Where `M` is the midpoint and the given points are:

`(color(red)(x_1), color(red)(y_1))` and `(color(blue)(x_2), color(blue)(y_2))`

Substituting the values from the points in the problem gives:

`M = ((color(red)(5sqrt(2)) + color(blue)(sqrt(2)))/2 , (color(red)(2sqrt(3)) + color(blue)(2sqrt(3)))/2)`

`M = ((color(red)(5sqrt(2)) + color(blue)(1sqrt(2)))/2 , (color(red)(2sqrt(3)) + color(blue)(2sqrt(3)))/2)`

`M = ((5 + 1)sqrt(2))/2 , ((2 + 2)sqrt(3))/2)`

`M = ((6sqrt(2))/2 , (4sqrt(3))/2)`

`M = (3sqrt(2) , 2sqrt(3))`