Question

The line segment AB joining the points A(2,-4) and B(5,2) is trisected at the points C(3,a) and D(b,a) .Find value of a & B??

Answer 1

Here is your answer......

Answer 2

Answer:

The value of a is -4 and b is 4 .        

Step-by-step explanation:

We are given that The line segment AB joining the points A(2,-4) and B(5,2) is trisected at the points C(3,a) and D(b,a)

C is the mid point of A and D

So, using mid point formula

$x=\frac{x_1+x_2}{2} ,y=\frac{y_1+y_2}{2}$

$A=(x_1,y_1)=(2,-4)$

$D=(x_2,y_2)=(b,a)$

$x=\frac{b+2}{2} ,y=\frac{a-4}{2}$

So, the coordinates of C is $x=\frac{b+2}{2} ,y=\frac{a-4}{2}$

We are given that the coordinates of C =(3,a)

On comparing

$\frac{b+2}{2}=3$               $\frac{a-4}{2}=a$              

$b=4$                                 $a=-4$    

Hence the value of a is -4 and b is 4 .