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stepladder [879]
3 years ago
13

PLEASE HELP! :D 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 steps you took to find the orthocenter, including any necessary points or slope you had to derive.
(I know the exact answer. I know the slopes and the point slope form, but I am basically having trouble with the plotting out the altitudes from the given points. Massive brain fart...)
Mathematics
1 answer:
OverLord2011 [107]3 years ago
6 0
I'm pretty sure you can just use a Cartesian plane and since all of your points are (positive, positive) they'd all be in the First Quadrant (top right)
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Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The shortest distance from A to C is the hypotenuse of the right triangle AYC

Applying the Pythagoras Theorem

AC^{2}=AY^{2} +YC^{2}

step 1

Find the length YC (hypotenuse of the right triangle YBC)

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YC^{2}=YB^{2} +BC^{2}

substitute the given values

YC^{2}=6^{2} +15^{2}

YC^{2}=261

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step 2

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substitute the given values

AC^{2}=8^{2} +\sqrt{261}^{2}

AC^{2}=325

AC=\sqrt{325}\ units

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