SOLUTION: The line 3x+2y = 24 meets y- axis at A and x- axis at B. The perpendicular bisector of AB meets the line through (0, -1 ) parallel to x- axis at C. Then area of the triangle ABC i

Question 1091924: The line 3x+2y = 24 meets y- axis at A and x- axis at B. The perpendicular bisector of AB meets the line
through (0, -1 ) parallel to x- axis at C. Then area of the triangle ABC is
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
At A,,

A:(8,0)
At B,

B:(0,12)
The slope of AB is,

The perpendicular bisector to AB would have a slope,

and it goes through (0,-1),

So now is (0,-1) point C?
Here's a picture of the perpendicular bisector to AB through (0,-1) but now unless (0,-1) is point C, I'm confused as to where C would be.
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If that's the case,

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If not, please provide additional information.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
3x +2y = 24
:
the x intercept is (8,0) and the y intercept is (0,12)
:
2y = -3x +24
y =-3x/2 +12
:
the equation of the perpendicular bisector has a slope = negative reciprocal of the given line
:
y = 2x/3 +b
:
the midpoint of AB = (12/2, 8/2) = (6, 4)
:
we use the midpoint to find b
:
4 = 2(6)/3 +b
:
b = 0
:
y = 2x/3
:
we find point C by setting the two equations, y = 2x/3 and y = -1, equal to each other and solve for x
:
2x/3 = -1
2x = -3
x = -3/2 = -1.5
:
point C = (-3/2, -1)
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the distance(d) between end points (-1.5, -1) and (6, 4) is the altitude of triangle ABC
:
d = square root((6-(-1.5))^2 + (4-(-1))^2) = 9.0139
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d between points (0,8) and (12,0) is the length of the base
:
d = square root(64 + 144) = 14.4222
:
********************************************************************
Area of triangle ABC = (1/2) * 14.4222 * 9.0139 = 65.0001 approx 65
********************************************************************
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