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ICSE Class 9 Answered

Using section formula, show that the points A(7, -5) , B(9, -3) and C( 13 1)  are collinear
Asked by spkattruva | 30 Jan, 2019, 09:55: PM
answered-by-expert Expert Answer

Let a point B(9,-3) divides the line joining the points A(7,-5) and C(13,1) in the ratio 1:k as shown in figure.
 
as per section formula, x-coordinate of B = begin mathsize 12px style fraction numerator 13 plus 7 k over denominator 1 plus k end fraction space equals space 9 space space space space o r space 13 space plus space 7 k space equals space 9 plus 9 k space space space space o r space space space 4 space equals space 2 space k space space space o r space space k space equals 1 half end style
y-coordinate of B = begin mathsize 12px style fraction numerator 1 minus 5 k over denominator 1 plus k end fraction space equals space minus 3 space space space o r space space 1 minus 5 k space equals space minus 3 minus 3 k space space space space space space o r space space space space space space space space space 4 space equals space 2 k space space space space space space space space o r space space space k space equals 1 half end style
From x-coordinate and y-coordinate of B, we get same ratio of AB/BC. Hence all the three points A,B and C are collinear
Answered by Thiyagarajan K | 31 Jan, 2019, 01:43: PM

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