Question

a line passing through ( c,2c) and (-1,2) is perpendicular from the line 4x+2y+3=0 find the value of c

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Answer 1

If two lines are ⊥, product of their slope is - 1.

On comparing with y = mx + c, slope of 4x + 2y + 3 is (-2). Let the slope of required line be m₁.

⇒ (-2)m₁ = - 1      ⇒ m₁ = 1/2

slope of line formed by (-1, 2) and (c , 2c) = 1/2

⇒ (2c - 2)/(c - (-1)) = 1/2

⇒ (2c - 2)/(c + 1) = 1/2

⇒ 2(2c - 2) = 1(c + 1)

⇒ 4c - 4 = c + 1

⇒ 4c - c = 1 + 4

⇒ 3c = 5

⇒ c = 5/3

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