SOLUTION: A triangle has vertices at A(2, -1), B(-1, 1) and C(6,3). Find the length of its altitude drawn to the side AC.
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Question 1008239: A triangle has vertices at A(2, -1), B(-1, 1) and C(6,3). Find the length of its altitude drawn to the side AC.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The slope of is
,
and the equation of line in in point-slope form is
-->
We can convert to the slope-intercept form by solving for ;
-->-->--> .
The altitude to AC is the perpendicular segment from to line ,
so its length is the distance from point to line .
There is somewhere an ugly formula to calculate distance from a point to a line,
so we could plug numbers into that formula and be done.
Otherwise, since the altitude to is perpendicular to ,
the slope of that altitude is .
The altitude to is part of a line
with slope that contains point .
The equation of that line in point-slope form is
--> .
We can convert to the slope-intercept form by solving for ;
-->-->--> .
We can find point at the intersection of the two perpendicular lines
-->-->-->-->--> .
So the altitude is with ,
and the length of altitude is
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