Question

Show that the points A(4,2) B(7,5) and C(9,7) are three points lie on a same line​

Answer 1

Answer:

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Answer 2

Let the points be A(4, 2), B(7, 5) and C(9, 7). By the distance formula

AB² = (4−7)² + (2−5)²

= (−3)² + (−3)²

= 9+9=18

BC² = (9−7)² + (7−5)²

=2² + 2²

=4+4=8

CA² = (9−4)² + (7−2)²

= 5² + 5²

= 25+25=50

So, AB = 3√2 ; BC = 2√2 ; CA = 5√2

AB + BC = 5√2 = AC

Hence the points A, B and C are collinear.