Question

If 2x-3y-5=0 is the perpendicular bisector of the line segment joining (3,-4) and (a,b) then a+b is​

Answer 1

Answer:

First we can write the equation in the form of y=mx+c

therefore, y=−  

3

2

​  

x+  

3

5

​  

 

therefore the perpendicular line with slope m  

1

​  

 is

⇒ mm  

1

​  

=−1

⇒  

3

−2

​  

×m  

1

​  

=−1

⇒ m  

1

​  

=  

2

3

​  

 

therefore the equation for  given line is

y−  

3

1

​  

=  

2

3

​  

(x−1)

6y−2=9x−9

9x−6y=7                                                          (!)

2x+3y=5

The point of intersection is (  

13

17

​  

,  

39

31

​  

)

This is the midpoint of A and B(h,k).

So,  

2

h+1

​  

=  

13

17

​  

 

2

k+  

3

1

​  

 

​  

=  

13

17

​  

 

B is (  

13

21

​  

,  

39

49

​  

)

Explanation: