Question

Using distance formula show that point P(2,1) Q(8,-3)and R(-1,3) are collinear​

Answer 1

Given : Three points P(2,1) Q(8,-3)and R(-1,3)

To find: Prove that these points are collinear.

Solution:

• Now we have given three points P(2,1) Q(8,-3)and R(-1,3).

• Now calculating the distance between each of them, that is PQ, QR and PR, we have:

                   Distance = √( (x2-x1)^2 + (y2-y1)^2 )

                   PQ = √( (8-2)^2 + (-3-1)^2 )

                   PQ = √36 + 16

                   PQ = √52

                   QR = √( (-1-8)^2 + (3-(-3))^2 )

                   QR = √81 + 36

                   QR = √117

                   PR = √( (-1-2)^2 + (3-1)^2 )

                   PR = √9 + 4

                   PR = √13

• Now, PQ + PR = QR

                   √52 + √13 = √117

                   2√13 + √13 = 3√13

• Hence proved that the points are collinear.

Answer:

                     So by distance formula we proved that point P(2,1) Q(8,-3)and R(-1,3) are collinear​ .

Answer 2

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