Find the lengths of the sides of the triangle PQR. Is it a right triangle? Is it an isoseceles triangle?(a)P(3,−2,−3),Q(7,0,1),R(1,2,1)(b)P(

Question

Find the lengths of the sides of the triangle PQR. Is it a right triangle? Is it an isoseceles triangle?(a)P(3,−2,−3),Q(7,0,1),R(1,2,1)(b)P(2,−1,0),Q(4,1,1),R(4,−5,4)

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Clara 4 months 2021-10-13T22:24:21+00:00 1 Answer 0 views 0

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    2021-10-13T22:26:01+00:00

    Answer:

    (a) It is an isosceles triangle with sides of lengths: 6, 2√10, and 6 units.

    (b) It is a right-angled triangle with hypotenuse side of 3√5 units, and opposite and adjacent sides of 6 and 3 units

    Step-by-step explanation:

    (a) P(3,−2,−3), Q(7,0,1), R(1,2,1)

    |PQ| = √[(7-3)² + (0+2)² + (1+3)²]

    = √(4² + 2² + 4²)

    = √36

    = 6

    |QR| = √[(1-7)² + (2-0)² + (1-1)²]

    = √((-6)² + 2² + 0)

    = √40

    = 2√10

    |RP| = √[(3-1)² (-2-2)² (-3-1)²]

    = √[(2² + (-4)² + (-4)²]

    = √36

    = 6

    |PQ| = |RP|

    So, triangle is isosceles.

    (b) P(2,−1,0), Q(4,1,1), R(4,−5,4)

    |PQ| = √[(4-2)² + (1+1)² + (1-0)²]

    = √(2² + 2² + 1²)

    = √9

    = 3

    |QR| = √[(4-4)² (-5-1)² (4-1)²]

    = √[(0 + (-6)² + 3²]

    = √45

    = 3√5

    |RP| = √[(2-4)² + (-1+5)² + (0-4)²]

    = √((-2)² + 4² + (-4)²)

    = √36

    = 6

    |PQ|² + |RP|² = |QR|²

    So, triangle is right-angled

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