Properties of TriangleHard

Question

The vertex C of a triangle ABC is (4, - 1). The equation of altitude AD and Median AE are 2x - 3y + 12 = 0 and 2x + 3y = 0 respectively then slope of side AB is :-

Options

A.
B.
C.
D.None of these

Solution


AD and AE meet at A therefore intersection of these two lines will give the coordinates of A which is (-3, 2).
Let coordinates of B is (h, k)
⇒  Slope of BC × Slope of AD = - 1
⇒
⇒  3h + 2k = 10            ...(i)
Also mid point of BC lies on AE
⇒    satisfies 2x + 3y = 0
⇒  2h + 3k = - 5            ...(ii)
Solving (i) and (ii) we get h = 8 and k = - 7
Therefore, A = (-3, 2), B = (8, -7) and
C = (4, - 1)
∴ Slope  AB =

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