Question

A and B are the points a ( - 3, 4) and b(3, - 4) respectively then the coordinates of the points c on ab produced such that ac= 3bc.​

Answer 1

Answer:

Given that,

The coordinates of a and b are (-3,4) and (2,1) respectively.

The point c lies on produced line ab such that ac=2bc

So,

ac : bc= 2 : 1

We use external section formula to find the coordinates of the point c.

c(x,y)= ((m*x2-n*x1)/(m-n),(m*y2-n*y1)/(m-n))

We have,

m : n= 2 : 1

Now, substituting all the known values, we get

c(x,y)= ((2*2-1*(-3))/(2-1),((2*1-1*4)/(2-1))

Solving further, we see

c(x,y)= (7/1,-2/1)

c(x,y)= (7,-2)

Step-by-step explanation:

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Answer 2

The coordinates of c are ($\frac{3}{2}$,-2).

Given,

The coordinates of a is (-3,4) and b is (3,-4).

There is point c on ab such that, ac=2bc.

To Find,

The coordinates of c.

Solution,

We can solve this mathematical problem with the following process.

The formula for the internal section is as follows,

If the line two points A($x_{1}, y_{1}$) and B($x_{2}, y_{2}$) are divided into two parts at point  C with m:n ratio then the coordinates of C will be, = $\frac{mx_{2}+nx_{1} }{m+n} ,\frac{my_{2}+ny_{1} }{m+n}$.

So, here given, ac=3bc, means ac : bc= 3:1.

We use the internal section formula to find the coordinates of point c.

So , coordination of c will be, $\frac{3.(3)+1.(-3)}{3+1} , \frac{3.(-4)+1.(4)}{3+1}$

= $\frac{9-3}{4} , \frac{-12+4}{4}$

=$\frac{6}{4} ,\frac{-8}{4}$

=$\frac{3}{2}$,-2.

Hence, the coordinates of c are ($\frac{3}{2}$,-2)

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