Question

P(-2,3), Q(1,2), R(4,1) Determine whether the points are collinear.

Answer 1

yes the points are collinear

Answer 2

Let P(-2,3)=(x1,y1) , Q(1,2)=(x2, y2),

And R(4,1)=(x3,y3) ,

Area∆PQR

= 1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|

=1/2|(-2)[2-1]+1(1-3)+4(3-2)|

=1/2|(-2)1 + 1 (-2) + 4 × 1 |

= 1/2 | -2 - 2 + 4 |

= 1/2 × 0

= 0

Therefore ,

Area ∆PQR = 0

P, Q and are R are collinear points.

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