Question

If

p

1,

3

     

is the mid-point of the line segment joining the points (2, 0) and

2

0,

9

     

,

then show that the line 5x + 3y + 2 = 0 passes through the point (–1, 3p)

Answer 1

Midpoint of points P(2,0) and Q(0,29) is given by, (x1+x22,y1+y22)

Midpoint of P(2,0) and Q(0,29)  = (22,292) = (1,19)

Given (1,p3) is the midpoint of  points P(2,0) and Q(0,29)

So, p3 = 19p =13We have to show that ,Line 5x+3y+2=0..(1) 

passes through the point (−1,3×13)
Substituting the values of x = −1 and y =1 in equ (i),
 we get5(−1)+3(1)+2 = 0−5+3+2=0−5+5 = 0
LHS = RHS.
So, the given line 5x+3y+2=0 passes through the point (−1,1)

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