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

Open in App

Solution

Let A(1,-1), B(5,2) and (9,5) be the given points. Then,we have
$A B = \sqrt{{(5 - 1)}^{2} + {(2 + 1)}^{2}} = \sqrt{16 + 9} = 5$
$B C = \sqrt{{(5 - 9)}^{2} + {(2 - 5)}^{2}} = \sqrt{16 + 9} = 5$
and, $A C = \sqrt{{(1 - 9)}^{2} + {(- 1 - 5)}^{2}} = \sqrt{64 + 36} = 10$
Clearly, AC=AB+BC
Hence, A,B,C are collinear points.

Suggest Corrections

Similar questions

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

Show that the points (1, – 1), (5, 2) and (9, 5) are collinear. [2 MARKS]

(1, - 1), (5, 2), (9, 5)

Using the distance formula, show that the given points are collinear:

(i) (1, -1), (5, 2) and 9, 5 (ii) (6, 9), (0, 1) and (-6, -7)

(iii) (-1, -1), (2, 3) and (8, 11) (iv) (-2, 5), (0, 1) and (2, 3).

Join BYJU'S Learning Program