You are given the co-ordinates of the four points A(6, 2), B(2, 4), C(−6, −2) and D(−2, −4).

You are given the co-ordinates of the four points A(6, 2), B(2, 4), C(−6, −2) and D(−2, −4).

(i) Calculate the gradients of the lines AB, CB, DC and DA.
Hence describe the shape of the figure ABCD.

(ii) Show that the equation of the line DA is 4y − 3x = −10 and find the length DA.

(iii) Calculate the gradient of a line which is perpendicular to DA and hence find the equation of the line l through B which is perpendicular to DA.

(iv) Calculate the co-ordinates of the point P where l meets DA.

(v) Calculate the area of the figure ABCD.

Solution: