Question

A line segment AB is increased along its length by 25% by producing it to C on the side of B. If A and B have the coordinates (–2,–3) and (2,1) respectively, then find the coordinates of C.

Answer 1

Answer:

(3, 0)

Step-by-step explanation:

Hi,

Given coordinates of A (-2, -3) and B(2, 1)

Slope of line AB , m = tan ∅ = (1+3)/(2+2) = 1

=>cos ∅ = sin ∅ = 1/√2.

Lets consider the parametric form of equation of straight line AB

Say, if A (-2, 3) having slope m, then any point on the line AB at a given distance r from A is given by

(x + 2)/cos ∅ = (y + 3)/sin ∅ = r

But we know coordinates of B (2, 1), so lets find r (finding r is just to find the point lies on which side of A on the segment AB)

(2+2)/ 1/√2 = r

=> r = 4√2.

So, point B lies on the segment AB at a distance of 4√2 from A.

Now given that the length is increased by 25%

=> new r will be r(1 + 25%)

=5r/4 = 5√2

Hence , using parametric form of line AB,

(x + 2)/1/√2 = (y + 3)/1/√2 =5√2, we get

x = 3 and y = 2

Hence , coordinates of C are (3, 2).

Hope, it helped !