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.
Answer by anand429(138)   (Show Source):
You can put this solution on YOUR website! x-y-2=0 ---(i)
2x-5y-7=0---- (ii)
Multiplying eqn (i) by 2,
2x-2y-4=0 ---(iii)
Subtracting (ii) from (iii), we get,
3y+3=0
=> y = -1
Putting back, x= y+2 = 1
So, intersection pt. P is (1,-1)
Let the line through P with gradient 2 be given by,
y = 2x + c
Since it passes through P(1,-1)
-1 = 2*1 + c
=> c = -3
So the required line is
y = 2x - 3
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)
So, area of triangle OAB
= (1/2)*(3)*(3/2)
= 9/4 sq. units.
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