Five points lie on a straight line and another 4 points lie on another straight line that is parallel to the first one, how many different triangles can be made by linking these 9 points?
a.7
b.20
c.70
d.140
e.400
OA: C
Five points lie on a straight line
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To explain it
L1 has 5 points (a,b,c,d,e)
L2 has 4 points (w,x,y,z)
Consider point a on L1 and w on L2 - there are 4 triangles awb, awc, awd, awe. Similarly there will be 4 triangles for each point on L2
Now, think of this, there would be 6 more traingles for point a awx, awy, awz, axy, axz, ayz
In a nutshell No of traingles from each point on L1
= [(no of points on L2)*(no of remaining points on L1)] + 6
So no of triangles
from a = 22
from b = 18
from c = 14
from d = 10
from e = 6
Total = 70
L1 has 5 points (a,b,c,d,e)
L2 has 4 points (w,x,y,z)
Consider point a on L1 and w on L2 - there are 4 triangles awb, awc, awd, awe. Similarly there will be 4 triangles for each point on L2
Now, think of this, there would be 6 more traingles for point a awx, awy, awz, axy, axz, ayz
In a nutshell No of traingles from each point on L1
= [(no of points on L2)*(no of remaining points on L1)] + 6
So no of triangles
from a = 22
from b = 18
from c = 14
from d = 10
from e = 6
Total = 70
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