Question

The area of the triangle formed by the points A(4,0),B(10,0) and C(4,3) is
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Answer 1

Given:

The points A(4,0), B(10,0,) and C(4,3)

To find:

The area of the triangle which is formed by the points A, B, and C.

The formula used to find the area of a triangle with given points -

$\boxed{\red{\frac{1}{2}[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]}}$ unit sq.

So,

A(4,0) :  x₁ =4,   y₁ = 0

B(10,0) : x₂= 10, y₂ = 0

C(4,3) :   x₃ = 4, y₃ = 3

Now,

Putting the values of x and y respectively,

$=\frac{1}{2}[4(0-3)+10(3-0)+4(0-0)]$

$=\frac{1}{2}[4(-3)+10(3)+4(0)]$

$=\frac{1}{2}[(-12)+30+0]$

$=\frac{1}{2}\times [18]$

= 9

Hence,

The area of the triangle formed by the points is 9 unit sq.

Answer 2

Answer:

9 units²

Step-by-step explanation:

The points (given)

A(4,0) : x₁ =4, y₁ = 0

B(10,0) : x₂= 10, y₂ = 0

C(4,3) : x₃ = 4, y₃ = 3

TO FIND:

The area of the triangle formed by the given points

Now,

The area of a triangle whose vertices are A(x₁ , y₁), B(x₂ , y₂), and C(x₃ , y₃) are given-

= 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₂) + x₃(y₁ - y₂)] unit²

= 1/2[4(0-3) + 10(3-0) + 4(0-0)]

= 1/2[-12 + 30 + 0]

= 1/2[18]

= 9 units²