. (i) Show that the points (5, -3), (9, 5) and (11,9)
are collinear.
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Answer:
Step-by-step explanation:
Let A (x1, y1) = ( 5, - 3 ), B (x2, y2) = ( 9, 5 )and C (x3, y3) = ( 11, 9 )
By using area of the triangle formula,
Δ = 1/2 | x1 ( y2 - y3 ) + x2 (y3 - y1 ) + x3 ( y1 - y2 ) |
= 1/2 | 5 ( 5 - 9 ) + 9 ( 9 + 3 ) + 11 ( - 3 - 5 ) |
= 1/2 | 5 ( - 4 ) + 9 ( 12 ) + 11 ( - 8 )|
= 1/2 | - 20 + 108 - 88 |
= 1/2 | - 108 + 108 |
= 1/2 | 0 |
= 0
Hence, given points are collinear.
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