Straight Line Revision Questions

1. A is the point ( 7, 0 ), B is ( -3, -2 ) and C ( -1, 8 ). The Median CE and the altitude BD intersect at J.

a.) Find the equations of CE and BD. (6 marks)
b.) Find the co-ordinates of J. (2 marks)

2. A triangle ABC has vertices A ( 4, 8 ) , B ( 1, 2 ) and C ( 7, 2 ).

a.) Show that the triangle is isosceles. (2 marks)
b.) (i) The altitudes AD and BE intersect at H, where D and E lie on BC and CA reprectively. Find the coordinates of H. (7 marks)
     (ii) Hence show that H lies one quarter of the way up DA. (1 mark)

3. Find the equation of the perpendicular bisector of the line joining A ( 2, -1 ) and B ( 8, 3 ).  (4 marks)

4. P ( -4, 5 ) , Q ( -2, -2 ) and R ( 4, -1 ) are the vertices of triangle PQR. Find the equation of PS, the altitude from P.  (3 marks)

5. A circles passes through A ( -2, 3 ) and B ( 4, -1 ). Find the equation of the perpendicular to the chord AB. ( 4 marks)

6. ABCD is a square. A is the point with coordinates ( 3, 4 ) and ODC has equation y = (1/2)x.
a.) Find the equation of the line AD. (3 marks)
b.) Find the coordinates of D. (3 marks)
c.) Find the area of the square ABCD (2 marks)