document.write( "Question 990836: The lines x-y-2=0 and 2x-5y-7=0 intersect at point P. Find co-ordinates of point P. The line through P with gradient 2 meets the axis A and B. Calculate the area of triangle AOB. \n" ); document.write( "
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x-y-2=0 ---(i)
\n" ); document.write( "2x-5y-7=0---- (ii)
\n" ); document.write( "Multiplying eqn (i) by 2,
\n" ); document.write( "2x-2y-4=0 ---(iii)
\n" ); document.write( "Subtracting (ii) from (iii), we get,
\n" ); document.write( "3y+3=0
\n" ); document.write( "=> y = -1
\n" ); document.write( "Putting back, x= y+2 = 1
\n" ); document.write( "So, intersection pt. P is (1,-1)
\n" ); document.write( "Let the line through P with gradient 2 be given by,
\n" ); document.write( "y = 2x + c
\n" ); document.write( "Since it passes through P(1,-1)
\n" ); document.write( "-1 = 2*1 + c
\n" ); document.write( "=> c = -3
\n" ); document.write( "So the required line is
\n" ); document.write( "y = 2x - 3
\n" ); document.write( "For finding intersection with axes, putting x and y =0 separately, we get, the intersection points as A(0,-3) and B(3/2,0)
\n" ); document.write( "So, area of triangle OAB
\n" ); document.write( "= (1/2)*(3)*(3/2)
\n" ); document.write( "= 9/4 sq. units.
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