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

Answer:

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

Step-by-step explanation:

Answer:

MATHS

If the coordinates of the mid-points of the sides of a triangle are (1, 1), (2, -3) and (3, 4). Find its centroid.

November 22, 2019Kinkini Rarhi

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ANSWER

Let P(1, 1), Q(2, -3), R(3, 4) be the mid-points of sides AB, BC and CA respectively of triangle ABC. Let A(x1,y1),B(x2,y2)andC(x3,y3) be the vertices of triangle. ABC. Then,

P is the mid-point of BC

⇒2x1+x2=1,2y1+y2=1

⇒x1+x2=2andy1+y2=2....(i)

Q is the mid-point of BC

⇒2x2+x3=2,2y2+y3=−3

⇒x2+

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Answer 2

Answer :

›»› The given points P,Q and T form a Scalene traingle.

Given :

• The points P(4, 3) Q(-5, -1) and T(2, -2) are vetices.

To Find :

• The given points P,Q and T form what traingle ?

Required Solution :

To find this is what traingle, at first we will find PQ then we will find QT, after that we will find PT after all this We can conclude that all side.

Finding PQ :

$\tt{:\implies PQ = \sqrt{ {(4 + 5)}^{2} + {(3 + 1)}^{2} } }$

$\tt{:\implies PQ = \sqrt{ {(9)}^{2} + {(4)}^{2} } }$

$\tt{:\implies PQ = \sqrt{81 + 16} }$

$\tt{:\implies PQ = \sqrt{97} }$

$\bf{:\implies \underline{ \: \: \underline{ \orange{ \: \: PQ = 9.84 \: \: }} \: \: }}$

Finding QT :

$\tt{:\implies QT = \sqrt{ {(4 - 2)}^{2} + {(3 + 2)}^{2} } }$

$\tt{:\implies QT = \sqrt{ {(2)}^{2} + {(5)}^{2} } }$

$\tt{:\implies QT = \sqrt{4 + 25} }$

$\tt{:\implies QT = \sqrt{29} }$

$\bf{:\implies \underline{ \: \: \underline{ \orange{ \: \: QT = 5.38 \: \: }} \: \: }}$

Finding PT :

$\tt{:\implies PT = \sqrt{ {( - 5 - 2)}^{2} + {( - 1 + 2)}^{2} } }$

$\tt{:\implies PT = \sqrt{ {( - 7)}^{2} + {(1)}^{2} } }$

$\tt{:\implies PT = \sqrt{49 + 1} }$

$\tt{:\implies PT = \sqrt{50} }$

$\bf{:\implies \underline{ \: \: \underline{ \orange{ \: \: PT = 7.07 \: \: }} \: \: }}$

• If all sides are equal then it is an equilateral traingle.

• If two sides are equal and one side are different side then it is Isosceles traingle.

• If all sides are different side then it is Scalene triangle.

So let's see Which triangle is this...

$\tt{:\implies PQ = 9.84}$

$\tt{:\implies QT = 5.38}$

$\tt{:\implies PT = 7.07}$

$\bf{:\implies \red{9.84 \neq 5.38 \neq 7.07}}$

$\bf{:\implies \red{PQ\neq QT\neq PT}}$

In this case all sides are different so this traingle is Scalene triangle.

║Hence, the given points P,Q and T form a Scalene triangle.║