Do the point (3,2),(-2,-3) and (2,3) from a triangle ? If so, name the type of triangle formed.
Answers
Question
Do the point (3,2),(-2,-3) and (2,3) from a triangle ? If so, name the type of triangle formed.
GIVEN:
Three points
(3,2) , (-2,-3) , (2,3)
TO FIND:
Do these points form a triangle?, If yes then which type of triangle is formed?
SOLUTION:
There are two ways of finding while these points are forming triangle or not.
By plotting the points in a graph
By calculating the area of figure formed by these points.
So, here we will do it by finding the area
Using formula to calculate area of triangle
→ Area = 1/2 \mid∣ [ x_1x
1
( y_2y
2
- y_3y
3
) + x_2x
2
( y_3y
3
- y_1y
1
) + x_3x
3
( y_1y
1
- y_2y
2
) ] \mid∣
→ Area = 1/2 | [ 3 ( -3 - (3) ) + (-2) ( 3 - 2 ) + 2 ( 2 - (-3) ) ] |
→ Area = 1/2 | [ -18 - 2 + 10 ] |
→ Area = 1/2 | [ -10 ] |
→ Area = 5 sq. units
Since, the area of figure formed by three points is not zero, it means three points are forming a triangle.
Now,
Let us take
A ( 3,2 ) , B ( -2,-3 ) , C ( 2,3 )
Then, Finding distances using distance formula
Distance = √[ ( x₁ - x₂ )² + ( y₁ - y₂ )² ]
→ AB = √[ (3 - (-2))² + ( 2 - (-3))² ]
→ AB = √( 25 + 25 ) = √50 units
→ BC = √[ (-2 - 2)² + (-3 - 3)² ]
→ BC = √( 16 + 36 ) = √52 units
→ AC = √[ (3 - 2)² + (2 - 3)² ]
→ AC = √( 1 + 1 ) = √2 units
Here, by Considering the lengths of sides of triangle
we can conclude that, lengths of AB, BC, and AC are forming a Pythagorean triplet;
BC² = AB² + AC²
( √52 )² = ( √50 )² + ( √2 )²
It means these lines are forming a right angled triangle.
Answer:
Answer ⬇
There are two ways of finding while these points are forming triangle or not.
By plotting the points in a graph
By calculating the area of figure formed by these points.
So, here we will do it by finding the area
Using formula to calculate area of triangle
→ Area = 1/2 \mid∣ [ x_1x
1
( y_2y
2
- y_3y
3
) + x_2x
2
( y_3y
3
- y_1y
1
) + x_3x
3
( y_1y
1
- y_2y
2
) ] \mid∣
→ Area = 1/2 | [ 3 ( -3 - (3) ) + (-2) ( 3 - 2 ) + 2 ( 2 - (-3) ) ] |
→ Area = 1/2 | [ -18 - 2 + 10 ] |
→ Area = 1/2 | [ -10 ] |
→ Area = 5 sq. units
Since, the area of figure formed by three points is not zero, it means three points are forming a triangle.
Now,
Let us take
A ( 3,2 ) , B ( -2,-3 ) , C ( 2,3 )
Then, Finding distances using distance formula
Distance = √[ ( x₁ - x₂ )² + ( y₁ - y₂ )² ]
→ AB = √[ (3 - (-2))² + ( 2 - (-3))² ]
→ AB = √( 25 + 25 ) = √50 units
→ BC = √[ (-2 - 2)² + (-3 - 3)² ]
→ BC = √( 16 + 36 ) = √52 units
→ AC = √[ (3 - 2)² + (2 - 3)² ]
→ AC = √( 1 + 1 ) = √2 units
Here, by Considering the lengths of sides of triangle
we can conclude that, lengths of AB, BC, and AC are forming a Pythagorean triplet;
BC² = AB² + AC²
( √52 )² = ( √50 )² + ( √2 )²
It means these lines are forming a right angled triangle.