the points A(-5,,4),b(-7,6) and c (5,2) are the coordinates of right angled triangle .which angle is right angle?
find the lengths of each side. The longest is the hypotenuse
However I think you have a typo because a^2 is not equal to b^2+c^2
To determine which angle in the triangle is a right angle, we need to calculate the slopes of the two sides that form the angle. If the product of the slopes is -1, then those sides are perpendicular and the angle between them is a right angle.
Let's first calculate the slopes of the two sides AB and BC.
The slope formula is given by:
m = (y₂ - y₁) / (x₂ - x₁)
For side AB:
x₁ = -5, y₁ = 4
x₂ = -7, y₂ = 6
m₁ = (6 - 4) / (-7 - (-5))
= 2 / -2
= -1
For side BC:
x₁ = -7, y₁ = 6
x₂ = 5, y₂ = 2
m₂ = (2 - 6) / (5 - (-7))
= -4 / 12
= -1/3
Since the product of the slopes (m₁ * m₂ = -1 * (-1/3) = 1/3) is not -1, this means that the angle between sides AB and BC is not a right angle.
Therefore, the right angle must be between the remaining sides: AC and BC.