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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