If (1, p/3) is the mid-point of the line segment joining the points (2, 0) an (0, 2/9) then show that the line 5x + 3y + 2=0 passes through thevpoint (-1,3p).

Dear Student,

Midpoint of points P2,0 and Q0,29 is given by, x1+x22,y1+y22Midpoint of P2,0 and Q0,29  = 22,292 = 1,19Given 1,p3 is the midpoint of  points P2,0 and Q0,29So, p3 = 19p =13We have to show that ,Line 5x+3y+2=0       ....i, passes through the point -1,3×13Substituting the values of x = -1 and y =1 in equ i, we get5-1+31+2 = 0-5+3+2=0-5+5 = 0LHS = RHS.So, the given line 5x+3y+2=0 passes through the point -1,1

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