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
7.
coordinates of C.
how does 5:1 be the ratio .clear it out correctly ​

Answer 1

Answer:

The coordinates of point C is (3,2)(3,2)

Step-by-step explanation:

Given 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. we have to find the coordinates of point C

Let the length of line segment AB is x units.

It is given that AB is increased by 25% extended upto C.

Hence, BC=\frac{25}{100}\times x=\frac{1}{4}xBC=

100

25

×x=

4

1

x

∴ AB is externally divided into m:n i.e 5:1

By Section formula for external division

C=({\frac{(mx_2-nx_1)}{(m-n)},\frac{(my_2-ny_1)}{(m-n)}})C=(

(m−n)

(mx

2

−nx

1

)

,

(m−n)

(my

2

−ny

1

)

)

= ({\frac{(5(2)-1(-2))}{(5-1)},\frac{(5(1)-1(-3)}{(5-1)}})(

(5−1)

(5(2)−1(−2))

,

(5−1)

(5(1)−1(−3)

)

= (3,2)(3,2)