Question

If (-3 ,1) , (1 ,-3 ) and (2 ,3 ) then the area of triangle is *
a) 14 sq.units
b) 7 sq.units
c) 28 sq.units
d) 35 sq.units​

Answer 1

Answer:

option a is correct✅✔☑

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Question:-

If (– 3, 1), (1, – 3) and (2, 3) then the area of triangle is

(a) 14 sq.units.

(b) 7 sq.units.

(c) 28 sq.units.

(d) 35 sq.units.

Given:-

The coordinates of the vertices of the given triangle are:

A(x₁ = – 3, y₁ = 1).

B(x₂ = 1, y₂ = – 3).

C(x₃ = 2, y₃ = 3).

To Find:-

Area of a triangle.

Solution:-

We know that the area of the triangle whose vertices are (x₁, y₁), (x₂, y₂) and (x₃, y₃) is

$\sf \large |x_1(y_2 - y_3) + (x_2(y_3 - y_1) + x_3(y_1 - y_2)| </p><p>$

The given vertices of the triangle are

The given vertices of the triangle are

A(– 3, 1), B(1, – 3), and C(2, 3).

by using the above formula,

$\sf Area \: of \: triangle = \frac{1}{2} | - 3( - 3 - 3) + 1(3 - 1) + 2(1 - ( - 3))|$

$\sf Area \: of \: triangle = \frac{1}{2} |18 + 2 + 8|$

$\sf Area \: of \: triangle = \frac{1}{2} |28| \\ \sf Area \: of \: triangle = {{ \cancel{\frac{28}{2} }}}$

$\sf Area \: of \: triangle = 14.$

${ \boxed{ \sf \bold \red{ \underline{Hence, the \: area \: of \: triangle \: is (a) 14 \: sq.units. }}}}$