Question

How do you find the midpoint of (-3, 4) and (5, 4)?

Answer 1

`color(blue)("Mid point "-> (x,y) = (1,4)". ")`Notice that as `y=4` is true for each of the given points, this is a plot of a line parallel to the x-axis. So the equation of the line is: y=4.

Explanation:

`x_("mid point") -> 1/2`the distance between the `x` values added to the first `x` value

`y_("mid point")-> 1/2` the distance between the `y` values added to the first `y` value.

`color(brown)("Let "(x_1,y_1) -> (-3,4))`

`color(brown)("Let "(x_2,y_2)->(5,4))`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To determine "x_("mid point"))`

`x_("mid point") = x_1 + (x_2-x_1)/2" "=" "(-3)+(5-(-3))/2`

`color(blue)(x_("mid point") " "=" "1)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To determine "y_("mid point"))`

`y_("mid point")" "=" "y_1+(y_2-y_1)/2" "=" "4+(4-4)/2`

`color(blue)(y_("mid point")" "=" "4`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mid point `-> (x,y) = (1,4)`