Answer
Verified
481.5k+ views
Hint: Use distance formula for finding the length of sides and then apply the condition for triangle.
The given points in the question are $\left( {3,2} \right),\left( { - 2, - 3} \right)$and$\left( {2,3} \right)$.
Let $\left( {3,2} \right)$is denoted as point$A$, $\left( { - 2, - 3} \right)$as point $B$and $\left( {2,3} \right)$as point $C$.
Now, we can use the distance formula for finding out the distance between two points $\left( {{x_1},{y_1}} \right)$and $\left( {{x_2},{y_2}} \right)$, it is:
$ \Rightarrow D = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} $
Applying this formula, we can find out the distance between points. We’ll get:
$
\Rightarrow AB = \sqrt {{{\left( {3 + 2} \right)}^2} + {{\left( {2 + 3} \right)}^2}} = \sqrt {50} = 5\sqrt 2 , \\
\Rightarrow BC = \sqrt {{{\left( { - 2 - 2} \right)}^2} + {{\left( { - 3 - 3} \right)}^2}} = \sqrt {52} = 2\sqrt {13} , \\
\Rightarrow AC = \sqrt {{{\left( {3 - 2} \right)}^2} + {{\left( {2 - 3} \right)}^2}} = \sqrt 2 , \\
$
From this, we can see that:
$
\Rightarrow A{B^2} = {\left( {5\sqrt 2 } \right)^2} = 50, \\
\Rightarrow B{C^2} = {\left( {2\sqrt {13} } \right)^2} = 52, \\
\Rightarrow A{C^2} = {\left( {\sqrt 2 } \right)^2} = 2. \\
\Rightarrow B{C^2} = A{B^2} + A{C^2} \\
$
The sides are satisfying Pythagoras theorem. $AB$ is perpendicular to $AC$.
Therefore, the above points are forming a triangle and it is a right angled triangle.
Note: If one of the angles of a triangle is ${90^ \circ }$,then the triangle is called a right angled triangle.
If one of the angles of a triangle is greater than ${90^ \circ }$,then the triangle is called an obtuse angled triangle. And if all the angles of a triangle are less than ${90^ \circ }$,then the triangle is called acute angled triangle.
The given points in the question are $\left( {3,2} \right),\left( { - 2, - 3} \right)$and$\left( {2,3} \right)$.
Let $\left( {3,2} \right)$is denoted as point$A$, $\left( { - 2, - 3} \right)$as point $B$and $\left( {2,3} \right)$as point $C$.
Now, we can use the distance formula for finding out the distance between two points $\left( {{x_1},{y_1}} \right)$and $\left( {{x_2},{y_2}} \right)$, it is:
$ \Rightarrow D = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} $
Applying this formula, we can find out the distance between points. We’ll get:
$
\Rightarrow AB = \sqrt {{{\left( {3 + 2} \right)}^2} + {{\left( {2 + 3} \right)}^2}} = \sqrt {50} = 5\sqrt 2 , \\
\Rightarrow BC = \sqrt {{{\left( { - 2 - 2} \right)}^2} + {{\left( { - 3 - 3} \right)}^2}} = \sqrt {52} = 2\sqrt {13} , \\
\Rightarrow AC = \sqrt {{{\left( {3 - 2} \right)}^2} + {{\left( {2 - 3} \right)}^2}} = \sqrt 2 , \\
$
From this, we can see that:
$
\Rightarrow A{B^2} = {\left( {5\sqrt 2 } \right)^2} = 50, \\
\Rightarrow B{C^2} = {\left( {2\sqrt {13} } \right)^2} = 52, \\
\Rightarrow A{C^2} = {\left( {\sqrt 2 } \right)^2} = 2. \\
\Rightarrow B{C^2} = A{B^2} + A{C^2} \\
$
The sides are satisfying Pythagoras theorem. $AB$ is perpendicular to $AC$.
Therefore, the above points are forming a triangle and it is a right angled triangle.
Note: If one of the angles of a triangle is ${90^ \circ }$,then the triangle is called a right angled triangle.
If one of the angles of a triangle is greater than ${90^ \circ }$,then the triangle is called an obtuse angled triangle. And if all the angles of a triangle are less than ${90^ \circ }$,then the triangle is called acute angled triangle.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE