1. Math
2. Calculus
3. find the lengths of the sides of the and8710pqr isandnbspand8710pqr...

# Question: find the lengths of the sides of the and8710pqr isandnbspand8710pqr...

###### Question details

Find the lengths of the sides of the $∆$PQR. Is $∆$PQR right-angled? Is $∆$PQR isosceles? P(2, −1, −0), Q(4, 1, 1) and R(4, −5, 2).

So I tried to calculate the distance between PQ QR and PR to prove they are Isosceles or right-angled triangle(by Pythagoras theorem)

by using formula $\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left(y}^{}}$2-y1)2+(z2-z1)2

and I calculated

$\overline{\mathrm{PQ}}$$\sqrt{{\left(4-2\right)}^{2}+{\left(-1-1\right)}^{2}+\left(1-{\left(-0\right)\right)}^{2}}$

1st question, How do I calculate $\left(1-{\left(-0\right)\right)}^{2}$  isn't Negative zero same as zero?
(assume -0 is not a typo)

$\overline{PR}$$\sqrt{{\left(4-2\right)}^{2}+{\left(-5+1\right)}^{2}+\left(2-{\left(-0\right)\right)}^{2}}$(Just going to assume 0 = -0 )

= $\sqrt{24}$

$\overline{QR}$ = $\sqrt{{\left(4-4\right)}^{2}+{\left(-6\right)}^{2}+{\left(1\right)}^{2}}$

= $\sqrt{37}$

2nd question, Could you please check my calculations are correct because I don't see any values to prove that $∆PQR$ is not isosceles or Right-angled Triangle.

Please include worked solution if my approach is wrong
Thank you!

###### Solution by an expert tutor 