Examine the collinearity of the following set of point: P(3, −5), Q(6, 1), R(4, 2) - Mathematics and Statistics

Examine the collinearity of the following set of point:

P(3, −5), Q(6, 1), R(4, 2)

Sum

Here, P(x₁, y₁) ≡ P(3, −5), Q(x₂, y₂) ≡ Q(6, 1), R(x₃, y₃) ≡ R(4, 2)

If A(ΔPQR) = 0, then the points P, Q, R are collinear.

∴ A(ΔPQR) = `1/2|(3, -5, 1),(6, 1, 1),(4, 2, 1)|`

= `1/2[3(1 - 2) - (-5)(6 - 4) + 1(12 - 4)]`

= `1/2[3(-1) + 5(2) + 1(8)]`

= `1/2(-3 + 10 + 8)`

= `15/2 ≠ 0`

∴ The points P, Q, R are non-collinear.

shaalaa.com

Application of Determinants - Area of Triangle and Collinearity of Three Points

Is there an error in this question or solution?

Chapter 4: Determinants and Matrices - Exercise 4.3 [Page 75]

Chapter 4 Determinants and Matrices
Exercise 4.3 | Q 8. (ii) | Page 75

Find the area of triangle whose vertices are

A(5, 8), B(5, 0) C(1, 0)

Find the area of triangle whose vertices are

`"P"(3/2, 1), "Q"(4, 2), "R"(4, (-1)/2)`

Find the area of triangle whose vertices are

M(0, 5), N(−2, 3), T(1, −4)

Find the area of quadrilateral whose vertices are

A(−3, 1), B(−2, −2), C(3, -1), D(1, 4)

Find the value of k, if the area of triangle whose vertices are P(k, 0), Q(2, 2), R(4, 3) is `3/2 "sq.unit"`

Examine the collinearity of the following set of point:

A(3, −1), B(0, −3), C(12, 5)

Examine the collinearity of the following set of point:

`"L"(0, 1/2), "M"(2, -1), "N"(-4, 7/2)`

Select the correct option from the given alternatives:

If A(0,0), B(1,3) and C(k,0) are vertices of triangle ABC whose area is 3 sq.units then value of k is