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Show that the points (1, 1), (2, 3) and (5, 9) are collinear. - Mathematics

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Question

Show that the points (1, 1), (2, 3) and (5, 9) are collinear.

Sum
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Solution

Given: Points A(1, 1), B(2, 3) and C(5, 9).

`AB = sqrt((2 - 1)^2 + (3 - 1)^2` 

= `sqrt(1 + 4)`

= `sqrt(5)` 

`BC = sqrt((5 - 2)^2 + (9 - 3)^2` 

= `sqrt(9 + 36)`

= `sqrt(45)` 

= `3sqrt(5)`

`AC = sqrt((5 - 1)^2 + (9 - 1)^2` 

= `sqrt(16 + 64)`

= `sqrt(80)`

= `4sqrt(5)`

Now `AB + BC = sqrt(5) + 3sqrt(5)` 

= `4sqrt(5)` 

= AC

AB + BC = AC, so the three points A(1, 1), B(2, 3) and C(5, 9) are collinear.

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Chapter 19: Co-ordinate Geometry: An Introduction - Exercise 19D [Page 404]

APPEARS IN

Nootan Mathematics [English] Class 9 ICSE
Chapter 19 Co-ordinate Geometry: An Introduction
Exercise 19D | Q 17. | Page 404
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