What is the area of the area of the triangle formed by the intersection of y = 2x-2, y = -1/2x + 8 and y=0 ?
a)45
b)67
c)89
d)31
e)37
a)45
b)67
c)89
d)31
e)37
The most straightforward way to find the area of a triangle is by multiplying base * height and dividing by 2.
So if there is a not too challenging way to get a base and height of this triangle, we are set.
Here are the three lines that intersect to form the triangle.
y = 2x - 2
y = -1/2x + 8
y = 0
y = 0 is the x axis and is a horizontal line, so the side of the triangle that lies on this line seems to be a great choice for the base. Now we need the length of the base.
y = 2x - 2 intersects the x axis when y = 0. y = 0 when x = 1.
y = -1/2x + 8 intersects the x axis when x = 16.
So the base of the triangle goes from point (1,0) to point (16,0) and is 16 - 1 = 15 long.
To get the height. first find the other vertex of the triangle.
Set the two equations, y = 2x - 2 and y = -1/2x + 8 equal to each other.
2x - 2 = -1/2x + 8
2 1/2x = 10
x = 4
y = 2(4) - 2 = 6
Since the base is at y = 0 and the y coordinate of the other vertex is 6, the height is 6.
bh/2 = (15*6)/2 = 45
The correct answer is A.
