First slide

Cartesian plane

Question

The points $(1, 1), (- 2, 7) a n d (3, - 3)$

Moderate

A

From a right angled triangle
B

From an isosceles triangle
C

Are collinear
D

Scalene

Solution

Let $A (1, 1), B (- 2, 7) a n d C (3, - 3)$ be the given points, then
$A B = \sqrt{{(- 2 - 1)}^{2} + {(7 - 1)}^{2}} = \sqrt{9 + 36} = 3 \sqrt{5}$

$B C = \sqrt{{(3 + 2)}^{2} + {(- 3 - 7)}^{2}} = \sqrt{25 + 100} = 5 \sqrt{5}$

$A C = \sqrt{{(3 - 1)}^{2} + {(- 3 - 1)}^{2}} = \sqrt{4 + 16} = 2 \sqrt{5}$

Clearly $B C = A B + A C,$

$\Rightarrow$ A,B,C are collinear.

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