Suppose P and Q lie on 3 x+4 y-4=0 and 5 x-y-4=0 respectively. If the mid-point of P Q is (1,5) , then the slope of the line passing through P and Q is

Step-by-step solution

Let the line P Q be. y-5=m(x-1) ...(i) Substituting y=m x+5-m in the equation 5 x-y-4=0 We have, .5 x-m x-5+m-4=0 (5-m) x+m-9=0 Therefore, x= 9-m 5-m and y=m ( 9-m 5-m )+5-m= 25-m 5-m Here, Q= ( 9-m 5-m , 25-m 5-m ) Substituting y=m x+5-m in the equation 3 x+4 y-4=0 We have, 3 x+4(m x+5-m)-4=0(3+4 m) x+16-4 m=0 Therefore, x= 4 m-16 4 m+3 and y= m(4 m-16) 4 m+3 +5-my= m+15 4 m+3 Hence, P= ( 4 m-16 4 m+3 , m+15 4 m+3 ) Since, m(1,5) is the mid-point of P Q , we have I= 1 2 [ 9-m 5-m + 4 m-16 4 m+3 ] .......(ii) and 5