Find the length of ab
a (2,-4) b (6,2)
solve for x and y
2x+3y+14
-4x+2y+4
given that b is the midpoint of segment ac and a (3,-2) and b (1,1), find c

FIRST QUESTION
Given points are:
A(2, -4)  and B(6, 2)
Now,  Use the distance formula.
distance formula = 
 
Now, plug the values into the formula, So,
distance  = 
               
                = 
    
                = 
 
                = 
 
                = 
  
               = 

So, the length of AB is .

THIRD QUESTION
Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.

Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint = 
        


Now, equaling the ordered pair, we have,

 .............equation (1)   

 ................equation (2) 

Now, taking equation (1)








Now, taking equation (2)








So, the co ordinates of C are (a, b) which is (-1 , 4)


SECOND QUESTION:
Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1

Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4

So, x=1 and y=4