Find the lengths of the sides of the triangle pqr p0 3 5 q6...

Find the lengths of the sides of the triangle PQR. P(0, -3, -5), Q(6, 0, 1), R(9, -6, -5) |PQ| = |QR| = |RP| = Is it a right triangle? Yes or No Is it an isosceles triangle? Yes or No

Transcript

00:01 Hi, in this question, given that point p is 0, -3, -5 and q is 6 ,0 ,1 and or is 9, -6, -5.

00:17 First we have to evaluate modulus pq which is equal to by using the distance formula square root of 6 -0 the whole square plus 0 plus 3 the whole square plus 1 minus into minus plus 5 the whole square.

00:34 On simplifying which is equal to square root of 6 square plus 3 square plus 6 square.

00:45 So which is equal to square root of 81 which is equal to 9.

00:49 Next we have to calculate modulus qr which can be written as square root of we have to use this two points.

00:58 So 9 -6 the whole square plus minus 6 minus 0 the whole square plus minus 5 minus 1 the whole square.

01:06 On further simplify which is equal to square root of here 9 minus 6 becomes 3, 3 square becomes 9 plus minus 6 the whole square becomes 36 plus minus 5 minus 1 becomes minus 6 minus 6 the whole square becomes 36 which is equal to square root of 81 which is equal to 9.

01:25 And finally we have to calculate modulus rp which is equal to square root of 0 minus 9 the whole square plus minus 3 minus 6 the whole square plus minus 5 plus 5 the whole square.

01:39 On further simplify which is equal to square root of 81 plus 9 which is equal to square root of 90 which is equal to 3 square root of 10.

01:48 Next we have to check whether it is right angle triangle or not.

01:53 So here by using the pythagoras theorem we can write it as a square plus b square equals c square...

Question

Find the lengths of the sides of the triangle PQR. P(0, -3, -5), Q(6, 0, 1), R(9, -6, -5) |PQ| = |QR| = |RP| = Is it a right triangle? Yes or No Is it an isosceles triangle? Yes or No

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