32) ABC is a triangle with vertices A (4, 8), B (7, 3) and C (3, 1). Find the equation of the median AD.
Since, the median includes point A, the coordinates of point A should satisfy the equation of the median. Hence, just check which amongst the equations is satisfied by the coordinates of point A (4, 8).
x + y = 4 + 8 = 12
7
x + y = 4 + 8 = 12
10
3x + y = 3 x 4 + 8 = 20
10
2x + y = 2 x 4 + 8 = 16 =16
6x + y = 6 x 4 + 8 = 32 =32
As can be seen, that only options‘d and ‘5’ are satisfied by the coordinates of point A, thus we can eliminate options ‘1’, ‘2’ and ‘3’.
Since we are left with two options, we need to do further elimination. This can be done by substituting the coordinates of point D.
Coordinates of point D can be found mentally as it is the average value of the corresponding coordinates of point B and C (D being the midpoint of B and C).
Now, checking between the options’4’ and ‘5’ which one is getting satisfied with the coordinates of point D (5, 2).
2x + y = 2x5 + 2 = 12
16
6x + y = 6x5 + 2 = 32 =32
Hence the answer is option ‘5’.