How to Find the Coordinates of the Vertex?

In mathematics, we study different types of shapes like Parallelogram, quadrilateral, triangle etc. Here we will see how to find the coordinates of the vertex of any shape. Here we will see case of triangle. Here we need to follow some steps to find coordinates of triangle.
Step 1: To find coordinate of vertices first of all assume three equations of lines. So equation of lines are 5x – 3y = -7, x + 2y = 9 and 3x – 7y = 1.
Step 2: Then solve any one equation and find value of ‘x’ or ‘y’. So using second equation x + 2y = 9, we can easily find value of ‘x’. So we can write equation as: x = -2y + 9.
Step 3: Now put value of ‘x’ in first equation. On putting value we get: 5x – 3y = -7.
= 5 (-2y + 9) – 3y = -7, => -10y + 45 – 3y = -7,
= -13y + 45 = -7, so here we get value of y = 4.
Step 4: Now put value of ‘y’ in equation (1). On putting value we get.
= 5x – 3 (4) = -7,
= 5x – 12 = -7, here we get value of 'x' is 1. So value of 'x' and 'y' coordinate is (1, 4) respectively. Now check the answer.
Step 5: Put 'x' and y- coordinate values in equation. On putting value we get:
= 5 (1) – 3 (4) = 5 – 12 = -7. So this is correct. Now check second equation.
= 1 + 2 (4) = 1 + 8 = 9. This coordinate is also correct.
Step 6: Then find Intersection of both equations. For next coordinate value we will apply the same procedure to other two equations and get the coordinate.