Answer :

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


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