Equation of line Solution9



In this page equation of line solution9 we are going to see solution of each problem with detailed explanation of the worksheet slope of the line.

(19) If A(3,6) and C(-1,2) are two vertices of rhombus AB,then find the equation of straight line that lies along the diagonal BD.

Solution:

In any rhombus two diagonals bisect each other and they are perpendicular to each other.

Midpoint of AC = Midpoint of BD

midpoint = (x₁ + x₂)/2 , (y₁ + y₂)/2

            = (3 - 1)/2 , (6 + 2)/2

            = (2/2),(8/2)

            = (1 , 4)

Slope of AC = (y₂ - y₁)/(x₂ - x₁)

                = (2-6)/(-1-3)

                = -4/(-4)

                = 1

Slope of BD = -1/1

                = -1

Equation of BD

(y - y₁) = m(x - x₁)

(y - 4) = -1 (x - 1)

y - 4 = - x + 1

x + y - 4 - 1 = 0

x + y - 5 = 0


(20) Find the equation of the line whose gradient is 3/2 and which passes through P, where  divides the line segment joining A(-2,6) and B(3,-4) in the ratio 2:3

Solution:

Slope of the line = 2/3

The point P divides the line segment joining A(-2,6) and B(3,-4) in the ratio 2 : 3

                      = (L x₂ + m x₁)/(L + m) , (L y₂ + m y₁)/(L + m)

                      = [2(3) + 3 (-2)]/(2 + 3) , [2(-4) + 3 (6)]/(2 + 3)

                      = [6 - 6]/5 , [-8 + 18]/5

                      = 0/5 , 10/5

                      = (0 , 2)

Equation of the line:

(y - y₁) = m (x - x₁)

(y - 2) = (2/3) (x - 0)

3 (y - 2) = 2 x

3 y - 6 = 2x

2 x - 3 y + 6 = 0

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