Question

A line segment AB is increased along it’s length by 25%by producing it to c on the side of B .if A and B have the co ordinate (1,2)and(5,6) respectively then find the co ordinate of c.

Answer 1

Answer:

d(A,B) = √ (5-1)² + (6-2)²

= √ 16 + 16

= 4√2

d(B,C) = 25 % d(A,B)

= 25/100 x 4√2

= √2

d(A,C) = d(A,B) + d(B,C)

=4√2 + √2

= 5√2

now , taking B as a point on line AC ,

AB : AC 4 : 1

m:n = 4:1

By section formula

x = mx2+ nx1/m+n

5 = 4(x2) + 1 / 4+1

25 = 4x2 + 1

x2 = 6

y = my2 + ny1/m+n

6 = 4(y2) + 2/4+1

6 = 4y2 + 2 /5

30 = 4y2 + 2

y2 = 7

co-ordinate of point C = (x2,y2) = (6,7)