Find the area of triangle whose vertices are A(5, 8), B(5, 0) C(1, 0) - Mathematics and Statistics

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