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Problem 9 Medium Difficulty

Find the lengths of the sides of the triangle $ PQR $. Is it a right triangle? Is it an isosceles triangle?

$ P (3, -2, -3) $ , $ Q (7, 0, 1) $ , $ R (1, 2, 1) $

Answer

$|P Q|=6,|Q R|=2 \sqrt{10},|P R|=6, \mathrm{PQR}$ is isosceles triangle.

Discussion

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KP

Kyle P.

May 12, 2020

explain

Video Transcript

feelings of the side of the triangle. We want to figure out whether it's right or ice Australis. All right, so let's find the length between P and Q. This is square root of three minus seven squared, plus native to minus zero squared, plus native three minus one square. Okay, sends up being sixteen plus for plus four. Um, I'm tired plus sixteen here in a CZ thirty six, which is six. Now. Let's find the length between Pienaar. Hey, so that's three nine x one squared, plus negative one. One is two squared, plus native, three minus one squared. Okay, so here will get here. We're going to get four hearing at sixteen, hearing another sixteen. Again. Get swear to thirty six, which is six. There's definitely I saw sleaze. Okay, there's two sides are equal. No need to find the length between Q and our. Okay, Q is seven. Then our is one squared plus zero minus two squared plus. Let's see. And they've got a one minus one squared. Hey, since I'm being square route forty just to read ten, so triangle looks like six. And that another six I got two Rad, huh? Okay, so it is not right, But it is my sausage. It was right. This would be Teo be six, right?