what we do when y=0

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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Tue Aug 13, 2013 9:06 pm

what is the area of the triangle formed by the intersection of y=2x-2, y=-1/2x+8 and y =0

OA is 45

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Source: Beat The GMAT — Problem Solving | Tue Aug 13, 2013 9:06 pm

ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Tue Aug 13, 2013 9:22 pm

sana.noor wrote:what is the area of the triangle formed by the intersection of y=2x-2, y=-1/2x+8 and y =0

OA is 45

I'm assuming the second equation is y = (-1/2)x + 8
y = 2x - 2
y = 0
2x = 2
x = 1
So point A = (1,0)

Similarly point B = (16, 0)

point C = (4, 6)

AC and BC are perpendicular to each other. (Lines y = 2x - 2 and y = (-1/2)x + 8)
AC = 3 sqrt(5)
BC = 6 sqrt(5)

Area = 1/2 * AC * BC
= 0.5 * 3 sqrt(5) * 6 sqrt(5)
= 9 * 5
= 45 square units

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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Tue Aug 13, 2013 9:30 pm

for the starters who cannot understand that how to reach at point C, here is the explanation.
put the two equations equal to each other
2x-2= (-1/2) =8 now solve for x
x= 4
put the value of x in any equation and one will get y= 6.
Now draw the diagram and find the area

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