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Question
Answer the following question:
Show that the following points are collinear by determinant:
P(5,1), Q(1,−1), R(11,4)
Solution
Here, P(x1, y1) ≡ P(5, 1), Q(x2, y2) ≡ Q(1,– 1), R(x3, y3) ≡ R(11, 4)
If A(ΔPQR) = 0, then the points P, Q, R are collinear.
∴ A(ΔPQR) = `1/2|(5, 1, 1),(1, -1, 1),(11, 4, 1)|`
= `1/2[5(-1 - 4) - 1(1 - 11) + 1(4 + 11)]`
= `1/2[5(-5) - 1(-10) + 1(15)]`
= `1/2(-25 + 10 + 15)`
= 0
∴ The points P, Q, R are collinear.
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