Question

b) Show that the points (8, 1) (3,-4) and (2,-5) are collinear using determinant.

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Answer 1

Answer:

If the area of the triangle ABC is zero then the points A,B,C are collinear

Area of triangle whose vertices are (X¹,Y¹) ,(X²,Y²), (X³, Y³) is

½ × | X¹( Y² –Y³ )+X² (Y³– Y¹) + X³ (Y¹– Y²)|

LET

(8,1) be. ( X¹, Y¹)

(3,–4) be. (X² ,Y²)

(2,–5) be. ( X³, Y³ )

Therefore area of triangle=

=½ × | 8{–4–(–5)} + 3(–5–1) + 2{1–(–4)}|

=½ ×|8×1+3×(–6)+2×5|

=½× |8 +(–18) +10|

=½× | 8+10–18|

=½× | 18–18|

=½×| 0 |

=½×0

= 0

Therefore the points are collinear