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A( 2, 1), B(5, 4) and C(2, 3) are the vertices of $ABC. AD, BE and CF are the altitudes of the triangle and M is the midpoint of BC. Match the items of Column I with those of Column II.Column IColumn II(A) Equation of AD is(p) x - y - 1 = 0 (B) Equation of BE is(q) x + 11 - 11 - 9 = 0(C) Equation of the median AM is(r) 7x + 3y - 5 = 0(D) Equation of the altitude CF is(s) x + 11y - 11 = 0(t) 3x + 7y -1 = 0 |
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Answer» (A) Slope of BC is 4 + 3/5 - 2 = 7/2 Therefore, the equation of the altitude AD is y - 1 = -3/7(x + 2) 3x + 7y - 1 = 0 Answer: (A) → (t) (B) Slope of CA is 1 + 3/-2 - 2 = -1 Therefore, the equation of the altitude BE is y - 4 = (x - 5) x - y - 1 = 0 Answer: (B) → (p) (C) The midpoint of BC is (7/2,1/2) and the slope of the median AM is -1/ 11 so that the equation of the median AM is y - 1 = -1/11(x + 2) x + 11y - 9 = 0 Answer: (C) → (q) (D) Lastly, the slope of AB is 4 - 1/5 + 2 = 3/7 and hence the equation of the altitude CF is y + 3 = -7/3(x - 2) 7x + 3y - 5 = 0 Answer: (D) → (r) |
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