MID-POINT E1

Find a and b if the midpoint of a line from (a, 6) to (8, b) is

(60, 70)

 

Solution

 

x1=a, x2=8, y1=6, y2=b.

 

(60, 70)= (x1 + x2, y1 + y2)

                   2             2

 

(60, 70)= (a + 8,  6 + b)

                  2          2

 

Equating equal values of x;

 

60= a + 8

         2      

 

2 x 60= (a + 8)  x 2 ¹

                2 ₁     

 

120 = a + 8

 

120-8 = a

 

a = 112.

 

Equating equal values of y;

 

70 = 6 + b

        2

 

2 x 70= (6 + b)  x 2 ¹  multiplying by 2 both sides.

                2 ₁     

 

140 = 6 + b

 

140 – 6 = b

 

b = 134

 

Hence a = 112 and b=134

 

TRY THIS……………………..

 

Find e and f if the midpoint of a line from (e, 19) to (13, f) is (10, 20)