# Find the equations of the two straight lines through (1, 2) forming two sides of a square of which 4x + 7y = 12 is one diagonal.

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Various Forms of Equations of line45 mins
Parametric Equations of Straight line48 mins
Straight line | Analyse your learning through quiz56 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
General Equation of a line43 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 1063 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses