An Important Question of class 10 Based on Equation of a Straight Line Chapter of M.L Aggarwal for ICSE BOARD.
Here three co-ordinate points of a triangle is given. Show that it is a right-angled triangle by using slopes.
This is the Question Number 26, Exercise 12.2 of M.L Aggarwal.
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Show that the triangle formed by the points A (1, 3), B (3, – 1) and C (– 5, – 5) is a right-angled triangle by using slopes.
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Given, points A (1, 3), B (3, – 1) and C (– 5, – 5) form a triangle
Now,
Slope of the line AB = m1 = (-1 – 3)/ (3 – 1) = -4/2 = -2
And,
Slope of the line BC = m2 = (-5 + 1)/ (-5 – 3) = -4/-8 = ½
Hence,
m1 x m2 = (-2) x (1/2) = -1
So, the lines AB and BC are perpendicular to each other.
Therefore, ∆ABC is a right-angled triangle.