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Question
If the orthocentre of the triangle formed by (1, 3) (4, –5) and (a, b) is (2, 4), Then the value of 33b + 22a is ______.
Options
0
`1/11`
1
`3/11`
MCQ
Fill in the Blanks
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Solution
If the orthocentre of the triangle formed by (1, 3) (4, –5) and (a, b) is (2, 4), Then the value of 33b + 22a is 1.
Explanation:
From the figure
Slope of BE = 1
Slope of AC = –1 ∴ (Slope of BE × slope of AC = –1)
∴ Equation AC is x + y = –1 ...(1)
Slope of CF = `(-9)/2`
Slope of AB = `2/9` ∴ (Slope of CF × slope of AB = –1)
∴ Equation AB is 2x – 9y = –25 ...(2)
Having (1) and (2) we get
(9, 6) = `((-34)/11, 33/11)`
∴ The value of 33b + 22a = 1
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Equations of Line in Different Forms - Equations of Internal and External by Sectors of Angles Between Two Lines Co-ordinate of the Centroid, Orthocentre, and Circumcentre of a Triangle
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