Q5 of 319 Page 23

Using the method of slopes show that the following points are collinear:

A(16, – 18), B(3, – 6), C(– 10, 6)

We have three points given A(16, – 18), B(3, – 6), C(– 10, 6)

To Prove: Given Points are collinear


Proof: AB[(16, – 18),(3, – 6)], BC[(3, – 6),(– 10, 6)], CA[(– 10, 6),(16, – 18)]


Formula used: The slope of the line =


The slope of line AB =


AB =


The slope of line BC =


BC =


The slope of line CA =


CA =


Here, AB = BC = CA


Hence, The Given points are collinear.


More from this chapter

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4

Find the slopes of a line

(i) which bisects the first quadrant angle


(ii) which makes an angle of 300 with the positive direction of y - axis measured anticlockwise.

 5

Using the method of slopes show that the following points are collinear:

A(4, 8), b(5, 12), C(9, 28)

 6

What is the value of y so that the line through (3, y) and (2, 7) is parallel to the line through (– 1, 4) and (0, 6) ?

 7

What can be said regarding a line if its slope is

(i) zero


(ii) positive


(iii) negative