CO-ORDINATE GEOMETRY - 3

A line passes through (2a, 7) and (8,5a). If its slope is 4, find a.

Solution

x1=2a, y1 = 7, x2 = 8, y2 = 5a

Slope(m) =    y2 – y1

                     x2 – x1

               4 =  5a – 7

                      8 – 2a

               4 =    5a – 7     [cross multiplying]

               1       8 – 2a

4(8 – 2a) = 5a – 7

32 – 8a = 5a – 7

32 – 8a + 7 = 5a

32 + 7 = 5a+ 8a

39 = 13a

39 = 13a

13     13

3 = a

Hence a = 3