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

###### Question details

Find the lengths of the sides of the $\u2206$PQR. Is $\u2206$PQR right-angled? Is $\u2206$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 $\sqrt{{({x}_{2}-{x}_{1})}^{2}+{(y}^{}}$_{2}_{1}_{2}_{1}

and I calculated

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

1st question, How do I calculate $(1-{(-0))}^{2}$ isn't Negative zero same as zero?

(assume -0 is not a typo)

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

= $\sqrt{24}$

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

= $\sqrt{37}$

2nd question, Could you please check my calculations are correct because I don't see any values to prove that $\u2206PQR$ is not isosceles or Right-angled Triangle.

Please include worked solution if my approach is wrong

Thank you!