Given triangle ghi with g(4.-3), h(-4,2), and i(2,4), find the perpendicular bisector of line hi in standard form.

Step-by-step explanation:

The perpendicular bisector is basically the line that intercept the side HI in its midpoint with a right angle. To find the equation of such line, we first have to find the slope of side HI, which coordinates are H(-4,2) and I(2,4)

Now, the condition of perpendicularity is

We replace the slope of HI to find the slope of the perpendicular bisector

We already have the slope of the perpendicular bisector, now we just a points that this line crosses. We know that a perpendicular bisector intercept the midpoint, so we have to find the midpoint of HI

Now we know the point we use the point-slope from to find the equation

Therefore, the standard form of the perpendicular bisector of line HI is

step-by-step explanation:

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