10. Show that the points (1,3), (2, 1) and (1/2,4) are collinear,by using using (i) concept of slope (ii) using a straight line and (3) any other method
Answers
Answer:
and 14 years Rs 10,000, Rs 8,000 and Rs 6,000. The money is invested in 3%, 6%, and 10% compound interest respectively. They will receive the amount when each of them attains the age of 21 years. Find using a five-figure log table, how much each would receive
Given : points (1,3), (2, 1) and (1/2,4) are collinear
To Find : Show by using (i) concept of slope (ii) using a straight line and (3) any other method
Solution:
(i) concept of slope
(1,3), (2, 1)
Slope = ( 1 - 3)/(2 - 1) = - 2
(1,3), (1/2,4)
Slope = ( 4 - 3)/ (1/2 - 1) = - 2
Hence slopes are equal
using a straight line
Distance between
(1,3) , (2 ,1 ) = √5
(1,3) , (1/2 ,4 ) = √5 /2
(2, 1) , (1/2 ,4 ) = 3√5 /2
√5 + √5 /2 = 3√5 /2
Segment Addition postulate works
Area points (1,3), (2, 1) and (1/2,4)
= (1/2) | 1 ( 1 - 4) + 2(4 - 3) + (1/2)(3 - 1)|
= (1/2) | -3 + 2 + 1 |
= 0
Area 0
hence points are collinear
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