The straight line L has equation 5x + 2y = 31
The point A has coordinates (0, 1)
The straight line M is perpendicular to L and passes through A.
Line L crosses the y-axis at the point B.
Lines L and M intersect at the point C.
Work out the area of triangle ABC.
You must show all your working.
Answers
Given : The straight line L has equation 5x + 2y = 31
The point A has coordinates (0, 1)
The straight line M is perpendicular to L and passes through A.
Line L crosses the y-axis at the point B.
Lines L and M intersect at the point C.
To Find : the area of triangle ABC.
Solution:
L is 5x + 2y = 31
The straight line M is perpendicular to L and passes through A. ( 0 , 1)
Slope of L = - 5/2
Hence slope of of M = 2/5
Equation of M is y - 1 = (2/5)(x - 0)
=> 5y - 5 = 2x
=> 2x - 5y = - 5
5x + 2y = 31 => 25x + 10y = 155
2x - 5y = - 5 => 4x - 10y = - 10
=> 29x = 145
=> x = 5
y = 3
Lines L and M intersect at the point C
Hence C = ( 5 , 3)
L crosses the y-axis at the point B.
5x + 2y = 31
=> x = 0 , y = 31/2
B = ( 0 , 31/2)
A. ( 0 , 1) , B = ( 0 , 31/2) , C = ( 5 , 3)
Area of triangle = (1/2)| 0 ( 31/2 - 3) + 0(3 - 1) + 5(1 - 31/2) |
= (1/2) | - 145/2 |
= 145/4 sq units
= 36.25 sq units
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