SOLUTION: decide whether the points are the vertices of a right triangle. (0,0), (0,3), (4,0)

Question 1035148: decide whether the points are the vertices of a right triangle. (0,0), (0,3), (4,0)
Found 2 solutions by Amrata1, MathTherapy:
Answer by Amrata1(11) (Show Source): You can put this solution on YOUR website!

Ans. Yes.
To check whether given coordinates form a triangle ,you can check either of this
1. All 3 points are non-collinear
2. Area of a triangle is non-zero
3. Sum of 2 sides is greater than 3rd side and difference of 2 sides is less than third side
In the give problem, clearly we are getting right angled triangle as there is
one line on x-axis of 3 units,
One line on y-axis of 4 units and making an angle of 90 degrees.
Both giving rise to 3rd line as hypotenuse of 5 units.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

decide whether the points are the vertices of a right triangle. (0,0), (0,3), (4,0)

Points (0, 0) and (0, 3), when joined, form a vertical line from the origin - a line that lies on the y-axis
Points (0, 0) and (4, 0), when joined, form a horizontal line from the origin - a line that lies on the x-axis
These lines are PERPENDICULAR, and so, form the legs of a right-angled triangle.
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