Question

the points P ( 4,3) Q ( -5,-1) and T ( 2,-2) are vertices of a
(a) Equilateral triangle
(b) Isosceles triangle
(c) Scalene triangle
(d) No triangle ​

Answer 1

$\huge\star\:\:{\orange{\underline{\pink{\mathbf{Solution:-}}}}}$

Finding the distance between the points,

(PQ)² = (-5-4)² + (-1-3)²

         = (-9)² + (-4)²

         = 81 + 16

         = 97

PQ =$\sqrt{97}$

Now,

(QT)² = (2+5)² + (-2+1)²

         = (7)² + (-1)²

         = 49 + 1

         = 50

QT =$\sqrt{50}$

And,

(PT)² = (2-4)² + (-2-3)²

         = (-2)² + (-5)²

         = 4 + 25

         = 29

PT =$\sqrt{29}$

So,

We can conclude that all side are different

PQ ≠ QT ≠ PT

Hence,

It is a Scalene triangle

Option c) Scalene triangle is correct

Answer 2

Answer:

ing the distance between the points,

ing the distance between the points,(PQ)² = (-5-4)² + (-1-3)²

ing the distance between the points,(PQ)² = (-5-4)² + (-1-3)² [tex] = (-9)² + (-4)²

= 81 + 16

= 81 + 16 = 97

= 81 + 16 = 97PQ = \sqrt{97}

= 81 + 16 = 97PQ = \sqrt{97} 97[/tex]

Now,

Now,(QT)² = (2+5)² + (-2+1)²

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)²

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50}

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)²

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)²

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)² = 4 + 25

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)² = 4 + 25 = 29

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)² = 4 + 25 = 29PT = \sqrt{29}

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)² = 4 + 25 = 29PT = \sqrt{29} 29

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)² = 4 + 25 = 29PT = \sqrt{29} 29

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)² = 4 + 25 = 29PT = \sqrt{29} 29

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)² = 4 + 25 = 29PT = \sqrt{29} 29 So,

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)² = 4 + 25 = 29PT = \sqrt{29} 29 So,We can conclude that all side are different

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)² = 4 + 25 = 29PT = \sqrt{29} 29 So,We can conclude that all side are differentPQ ≠ QT ≠ PT

Now,(QT)² = (2+5)² + (-2+1)² = (7)² + (-1)² = 49 + 1 = 50QT = \sqrt{50} 50 And,(PT)² = (2-4)² + (-2-3)² = (-2)² + (-5)² = 4 + 25 = 29PT = \sqrt{29} 29 So,We can conclude that all side are differentPQ ≠ QT ≠ PTHence,

Isosceles triangle

Step-by-step explanation:

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