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

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

Sum

Here, A(x₁, y₁) ≡ A(5, 8), B(x₂, y₂) ≡ B(5, 0), C(x₃, y₃) ≡ C(1, 0)

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

∴ A(ΔABC) = `1/2|(5, 8, 1),(5, 0, 1),(1, 0, 1)|`

= `1/2[5(0 - 0) - 8(5 - 1) + 1(0 - 0)]`

= `1/2[0 - 8(4) + 0]`

= `1/2(-32)`

= – 16

Since area cannot be negative,
A(ΔABC) = 16 sq. units

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

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

Chapter 4 Determinants and Matrices
Exercise 4.3 | Q 5. (i) | Page 75

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:

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