Coordinate geometry involves calculating the midpoint, slope, distance, and the equation of a line or line segment; you may also be required to find the intersection between two lines.
(a) Write down the coordinates of point A and point B on the diagram.
(b) Mark in the point D (6, 8) on the diagram.
(c) Find the co-ordinates of C, the midpoint of [AB].
(d) Join A to D. Join B to D. Join C to D.
(e) Use the distance formula to find |AD| and |BD| .
(f) What type of triangle is ABD? Give a reason for your answer.
Reason: The lengths of two sides are equal, | AD | = | BD |
(g) State whether the triangles ACD and BCD are congruent. Give a reason for your answer.
Answer:Yes, they are congruent
Reason: | AC | = | BC | as C is the midpoint of [AB]
| AD | = | BD | from part (e)
| CD | = | CD | common side
SSS - congruent triangles