8. The line \(l _ { 1 }\) has equation
$$2 x - 5 y + 7 = 0$$
- Find the gradient of \(l _ { 1 }\)
Given that
- the point \(A\) has coordinates \(( 6 , - 2 )\)
- the line \(l _ { 2 }\) passes through \(A\) and is perpendicular to \(l _ { 1 }\)
- find the equation of \(l _ { 2 }\) giving your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants to be found.
The lines \(l _ { 1 }\) and \(l _ { 2 }\) intersect at the point \(M\). - Using algebra and showing all your working, find the coordinates of \(M\).
(Solutions relying on calculator technology are not acceptable.)
Given that the diagonals of a square \(A B C D\) meet at \(M\), - find the coordinates of the point \(C\).