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velikii [3]
3 years ago
7

Triangle ABC has vertices A(0,6) B(4,6) C(1,3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the s

teps you took to find the orthocenter, including any necessary points or slope you had to derive.
Mathematics
1 answer:
Allisa [31]3 years ago
5 0

For line B to AC:  y - 6 = (1/3)(x - 4);  y - 6 = (x/3) - (4/3); 3y - 18 = x - 4, so 3y - x = 14

For line A to BC:  y - 6 = (-1)(x - 0);  y - 6 = -x, so y + x = 6

Since these lines intersect at one point (the orthocenter), we can use simultaneous equations to solve for x and/or y:

(3y - x = 14) + (y + x = 6) =>  4y = 20, y = +5;  Substitute this into y + x = 6:  5 + x = 6, x = +1

<span>So the orthocenter is at coordinates (1,5), and the slopes of all three orthocenter lines are above.</span>

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see below

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