Question

use determine to show that the following points are collinear
(i) A(2,3),B(-1,-2),C(5,8)
(ii) (-2,5),(-6,-7),(-5,-4)​

Answer 1

Answer:

(I)A(2,3), B(-1,-2), C(5,8)

area of∆ABC=1/2|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|

=1/2|2(-2-8)-1(8-3)+5(3+2)|

=1/2|2(-10)-1(5)+5(5)|

=1/2|-20-5+25|

=1/2|0|

=0/2=0

so the points are collinear.

(ii)P(-2,4), Q(-6,-4), R(-5,-4)

area of ∆PQR=1/2|-2(-7+4)-6(-4-5)-5(5+7)|

=1/2|-2(-3)-6(-9)-5(12)|

=1/2|6+54-60|

=1/2|0|

=0/2=0

so the points are collinear.