Question

Find the coordinates of the point C if the point B(1/2,6) divides the line segment joining the point A(3,5) and C in the ratio 1:3

Answer 1

Answer:

The coordinates point of C is

$( \frac{19}{8} . \: \frac{21}{4} )$

Step-by-step explanation:

The answer is explained in the image.

Answer 2

Answer:

The coordinates of point C are C(-7,9).

Step-by-step explanation:

Given that,

The point $B(\frac{1}{2},6)$ divides the line segment joining the point $A(3,5)$ and C in the ratio 1:3.

Let the unknown point be C(x,y).

We know that If a point $P(a,b)$ divides the join of two points $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$ in the ratio $m:n$ then its coordinates are given by

$P(a,b)=(\frac{mx_{2}+nx_{1}}{m+n} ,\frac{my_{2}+ny_{1}}{m+n} )$

Substituting the given values in the above formula we get

$B(\frac{1}{2},6)=(\frac{1(x)+3(3)}{1+3} ,\frac{1(y)+3(5)}{1+3} )$

Thus we shall write

$\frac{1}{2}=\frac{9+x}{4}= > 9+x=2\\= > x=-7$and

$6=\frac{15+y}{4}= > y=24-15=9$

Therefore,

The coordinates of point C are C(-7,9).

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