*l*passes through the points

*A*and

*B*with coordinates (2,0) and (5,6) respectively.

**a)**Find an equation of

*l*

*L*is perpendicular to

*l*and passes through the point

*C*with coordinates (0.5,7)

The lines

*l*and

*L*intersect in the point

*D*.

**b)**Find an equation of

*L*and show that the coordinates of

*D*are (4.5,5)

**c)**the ratio in which

*D*divides the line segment

*AB*

**d)**the area of triangle

*ABC*

Please show all your working, and include the names of any facts or theories you use. If possible, include a diagram. Thank you!