Question

find the area of the triangle formed by the points v(0,5) s(0,1) t(3,0)​

Answer 1

Answer:-

Given points are V (0 , 5) ; S (0 , 1) and T (3 , 0).

We know that;

Area of a triangle formed by the vertices (x₁ , y₁) ; (x₂ , y₂) and (x₃ , y₃) is:-

$\red{\sf Area _{ \Delta} = \dfrac{1}{2} \begin{vmatrix} \sf \: x_1 - x_2 \: & \sf \: x_1 - x_3 \\ \\ \sf \: y_1 - y_2 & \sf \: y_1 - y_3 \end{vmatrix}}$

Let;

• x₁ = 0

• y₁ = 5

• x₂ = 0

• y₂ = 1

• x₃ = 3

• y₃ = 0

Putting the respective values we get;

$\implies \sf Area _{ \Delta} = \dfrac{1}{2} \begin{vmatrix} \sf \: 0 - 0\: & \sf \: 0 - 3 \\ \\ \sf 5 - 1 & \sf \: 5 - 0 \end{vmatrix} \\ \\ \\ \implies \sf Area _{ \Delta} = \dfrac{1}{2} \begin{vmatrix} \sf \: 0\: & \sf \: - 3 \\ \\ \sf 4 & \sf \: 5 \end{vmatrix} \\ \\ \\ \implies \sf Area _{ \Delta} = \frac{1}{2} |0 \times 5 - ( - 3)(4)| \\ \\ \\ \implies \sf Area _{ \Delta} = \frac{1}{2} \times 12 \\ \\ \\ \implies \boxed{ \red{\sf Area _{ \Delta} =6 \: unit^{2} }}$

∴ The area of the given triangle is 6 unit².

Answer 2

Answer:

Given :-

• v(0 , 5)
• s(0 , 1)
• t(3 , 0)

To Find :-

• What is the area of the triangle.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{Area\: of\: the\: triangle =\: \dfrac{1}{2} \begin{vmatrix} \sf \: x_1 - x_2 \: & \sf x_1 - x_3 \\ \\ \sf \: y_1 - y_2 & \sf \: y_1 - y_3 \end{vmatrix}}}}$

Solution :-

Let's,

⋆ $\sf x_1 =\: 0$

⋆ $\sf x_2 =\: 0$

⋆ $\sf x_3 =\: 3$

⋆ $\sf y_1 =\: 5$

⋆ $\sf y_2 =\: 1$

⋆ $\sf y_3 =\: 0$

Now, by according to the question by using the formula we,

$\mapsto \sf Area\: of\: triangle =\: \dfrac{1}{2} \begin{vmatrix} \sf \: 0 - 0 \: & \sf 0 - 3 \\ \\ \sf \: 5 - 1 & \sf 5 - 0 \end{vmatrix}$

$\mapsto \sf Area\: of\: triangle =\: \dfrac{1}{2} \begin{vmatrix} \sf \: 0 \: & \sf -\: 3 \\ \\ \sf \: 4 & \sf 5 \end{vmatrix}$

$\mapsto \sf Area\: of\: triangle =\: \dfrac{1}{2} \begin{vmatrix} \sf 0 \times 5 - (- 3)(4) \end{vmatrix}$

$\mapsto \sf Area\: of\: triangle =\: \dfrac{1}{2} \begin{vmatrix} 0 - (- 3) \times 4 \end{vmatrix}$

$\mapsto \sf Area\: of\: triangle =\: \dfrac{1}{2} \begin{vmatrix} 3 \times 4 \end{vmatrix}$

$\mapsto \sf Area\: of\: triangle =\: \dfrac{1}{\cancel{2}} \times {\cancel{12}}$

$\mapsto \sf Area\: of\: triangle =\: 1 \times 6$

$\mapsto \sf\bold{\purple{Area\: of\: triangle =\: 6\: sq\: unit}}$

$\therefore$ The area of the triangle is 6 sq unit.