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 = m

_{1}= (-1 – 3)/ (3 – 1) = -4/2 = -2And,

Slope of the line BC = m

_{2}= (-5 + 1)/ (-5 – 3) = -4/-8 = ½Hence,

m

_{1}x m_{2}= (-2) x (1/2) = -1So, the lines AB and BC are perpendicular to each other.

Therefore, ∆ABC is a right-angled triangle.