Find the value of k, if the area of triangle whose vertices are P(k, 0), Q(2, 2), R(4, 3) is 32sq.unit - Mathematics and Statistics

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"`

बेरीज

Here, P(x₁, y₁) ≡ P(k, 0), Q(x₂, y₂) ≡ Q(2, 2), R(x₃, y₃) ≡ R(4, 3)

A(ΔPQR) = `3/2 "sq.units"`

Area of a triangle = `1/2|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|`

∴ `± 3/2 = 1/2|("k", 0, 1),(2, 2, 1),(4, 3, 1)|`

∴ `± 3/2 = 1/2["k"(2 - 3) - 0 + 1(6 - 8)]`

∴ `± 3/2 = 1/2(-"k" - 2)`

∴ ± 3 = –k – 2

∴ 3 = –k – 2 or –3 = –k – 2

∴ k = – 5 or k = 1

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

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पाठ 4: Determinants and Matrices - Exercise 4.3 [पृष्ठ ७५]

पाठ 4 Determinants and Matrices
Exercise 4.3 | Q 7 | पृष्ठ ७५

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)

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:

P(3, −5), Q(6, 1), R(4, 2)

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