Question: Am I missing something here? My homework says to prove that the given triangle is a right triangle, but it does not appear to be a right triangle mathematically.

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> Let $A =(-3, 2)$, $B=(1, 0)$, and $C=(4,6)$.
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> Prove that $\blacktriangle ABC$ is a right triangle. 
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I have tried the slope method and it didn't work, I also tried the distance (Pythagorean) method and that didn't work either.

Answer: 
[![enter image description here](https://i.stack.imgur.com/OgtCk.png)](https://i.stack.imgur.com/OgtCk.png)

Add points $D=(-3,0)$ and $E=(4,0)$ and show that $\Delta ABD \sim\Delta BCE$. Then show that $\measuredangle ABC=90^\circ$.

Do you see why the slopes of perpendicular lines are negative reciprocals of each other?
If you calculate again the distances you will see that
$$AC^2=AB^2+BC^2$$