(Solved): Linear equations The line \( A B \) passes through the points \( A(2,-5) \) and \( B(k, 7) \), whe ...

Linear equations The line \( A B \) passes through the points \( A(2,-5) \) and \( B(k, 7) \), where \( k \) is a constant. Given that the line \( A B \) is perpendicular to \( 3 x-4 y=8 \) a) Find the gradient of the line \( A B \). (2 marks) b) Find an equation for the line \( A B \) in the form \( a x+b y+c=0 \), where \( a, b \) and \( c \) are integers. marks) c) Determine the value of \( k \quad \) (2 marks) d) Hence, find the distance between points \( A \) and \( B \). (2 marks) e) Give the coordinates of the midpoint between \( A \) and \( B \). (2 marks)