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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