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Answer:
- altitude to A: x = -3
- altitude to B: 7x +6y = 36
- altitude to C: x +2y = 16
Step-by-step explanation:
The calculations are repetitive, so it can be useful to use a spreadsheet to do them.
Altitude to A
The altitude to point A will be the line perpendicular to BC through point A. A way to write that equation is ...
(Cx -Bx)x + (Cy -By)y = (Cx -Bx)(Ax) + (Cy -By)(Ay)
(4 -0)x + (6 -6)y = (4 -0)(-3) +(6 -6)(0)
4x = -12
x = -3 . . . . . . . simplify to standard form (divide by 4)
Performing similar calculations on the other points, we find the equations of the altitude lines to be ...
Altitude to B
-7x -6y = -36 . . . . has a common factor of -1
7x +6y = 36 . . . . . in standard form
Altitude to C
3x +6y = 48 . . . . has a common factor of 3
x +2y = 16 . . . . . . . in standard form
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Additional comment
Standard form requires the leading coefficient be positive, and all the coefficients be mutually prime.
