SOLUTION: The coordinates of {{{A}}} and {{{B}}} are (2,-4) and (0,3) respectively. {{{C}}} is a point on the line {{{L}}} such that the area of the triangle {{{ABC}}} is {{{8 unit^2}}}. Fin

Question 764907: The coordinates of and are (2,-4) and (0,3) respectively. is a point on the line such that the area of the triangle is . Find the two possible equation of .
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Line AB is y=-(7/2)x+3, and the line perpendicular to it at point (0,3) is y=(2/7)x+3. The point (0,3) here was picked arbitrarily for convenience.

Using segment AB as a base of the triangle, distance formula, steps here omitted,... the base AB is .
Triangle with 8 unit^2 will have an altitude value h, so that:

What point is h units away from (0,3) and is on line y=(2/7)x+3?
That refers to another distance and the use of distance formula again.
We want those two, variable points of (x, (2/7)x+3).
Applying distance formula,

which will simplify to:
.
.
or
From those two values, you can use to determine the corresponding values for y.

Can you finish the rest of the way to the needed line for some y-intercept g ?

------------------------------------------
Just to show final answer without the remaining steps,
lines wanted are:
and
and know that point C is really still a variable point.
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