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# Find the lengths of the sides of the triangle $PQR$. Is it a right triangle? Is it an isosceles triangle?$P (2, -1, 0)$ , $Q (4, 1, 1)$ , $R (4, -5, 4)$

## $|P Q|=3,|Q R|=3 \sqrt{5},|P R|=6, \mathrm{PQR}$ is a right triangle.

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Sittie H.

August 21, 2021

Determine whether or not the line through the points ????1 (4,8, 0),????2 (1,2, 3) is parallel to the line through the points ????1 (0, 5,0),????2 (?3,?1,3)

SH

Sittie H.

August 21, 2021

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### Video Transcript

So here we're giving information about a certain triangle. We have he with two comma negative one comma zero. A second point cute. Just four comma one comma one and our which is four common negative five common for so family, we have to apply distance form those three times here. So the distance of peak you would be The square root of 4 -2 squared plus uh two squared plus one squared. So it would be four minus two squared. Bridge is just four plus 1 -1 Skirt which should be it would be two squirts and I'd be four plus one. So The length of this side is equivalent to three and we're going to repeat this process for pr So for pr it'd be the square root of four plus 16 and plus 16 And we find as a result that this is equivalent to six. And now we're going to repeat this process for the third side and we can find that the third side is for my forces your a squared than us, -5 -1 Squared is there'd be 36 plus four minus one squared Which is three squares of the square roots of 36 plus nine. And we find that this is equivalent to the square root uh 45 Which is also equivalent to 3 sq3. Route five. So really to check if it's if this is a right triangle, we can we can take three used diagram here. Um and we see that essentially this angle would be a right angle. So this is a right triangle. And we see that this is not an isosceles triangle, considering the fact that we have, we don't have two sides that are equivalent, and this is our final answer.

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