MID-POINT 1

The midpoint of a line from (9, 2a) to (5, 5a) is (7, 7). Find a.

Solution

x1=9, x2=5, y1=2a, y2=5a.

Mid point = (x1 + x2, y1 + y2)

                         2            2

(7, 7) =   (9 + 5,  2a + 5a)

                  2          2

(7, 7) = (14, 7a)

              2    2

comparing the values of y;

7 = 7a

       2

2x7 = 7a x 2¹    [ multiplying by 2 on both sides]

          2₁

14 = 7a

²14 = 7a       [ dividing by 7 on both sides]

   7     7

a = 2

TRY THIS……………………..

The midpoint of a line from (3a, 5) to (9a, 11) is (18, 8).

Find a.