Find the equation

Given: 4x + 7y = 12 is one diagonal and opposite vertex is (1,2)

To find: equation of straight line

Explanation:

Let A (1, 2) be the vertex of square ABCD and BD be the diagonal that is along the line 4x + 7y = 12

Diagram:

Here, we have to find the equations of sides AB and AD, each of which makes an angle of 45∘ with line 4x + 7y = 12

We know that the equations of two lines passing through a point x1,y1 and making an angle α with the line whose slope is m.

Equation of given line is

4x + 7y = 9

m, x₁ = 1, y₁ = 2, α = 45∘

So, the equations of the required sides are

⇒ 3x – 11y + 19 = 0 and 11x + 3y – 17 = 0

Hence, equation of straight line 3x – 11y + 19 = 0 and 11x + 3y – 17 = 0