Question

Prove that three altitudes of a triangle meet at one point

Answer 1

Medals and Fan for Algebraic Resposne

Answer 2

@mathmate

Answer 3

Geometrically or algebraically?

Answer 4

Algebraiccly please

Answer 5

That means with analytic geometry?

Answer 6

using algebra

Answer 7

Without loss of generality (WLOG), we draw a triangle with one vertex at (0,0), one at (a,0) and the third in the first quadrant.

ok so far?

Answer 8

yep

Answer 9

We now need the three altitudes. How do you propose to calculate that?

Answer 10

i have no idea. help

Answer 11

1. calculate the slopes of each of the sides using the slope formula:
\(\large slope = \frac{y_2-y_1}{x_2-x_1}\)

Answer 12

Labelling the vertices should help:

Answer 13

Do you know the slope of AB?
@DeltaSquad

Answer 14

@DeltaSquad
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