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 ______.

विकल्प

• 0

• `1/11`

• 1

• `3/11`

Answer 1

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