Question

Question #d902d

Answer 1

`3x+y=14`

Explanation:

The line segment through the points `(2,3)` and `(5,4)`:

[1]`color(white)("XXX")`has a mid-point at `((2+5)/2,(3+4)/2)=(3.5,3.5)`

[2]`color(white)("XXX")`has a slope of `m=(Deltay)/(Deltax)=(4-3)/(5-2)=1/3`

The perpendicular bisector of this line segment:

[1]`color(white)("XXX")`passes through the midpoint `(3.5,3.5)`

[2]`color(white)("XXX")`has a slope of `-1/m=-3`

Using the slope-point form for the perpendicular
`color(white)("XXX")y-3.5=(-3)(x-3.5)`
or
`color(white)("XXX")3x+y=14`

Here is a picture to help verify the results: