Question

The area of a triangle with vertices
at (-4, -1), (1, 2) and (4, -3)
is:​

Answer 1

Answer:

Area of a triangle with vertices (x

1

,y

1

) ; (x

2

,y

2

) and (x

3

,y

3

) is

∣

∣

∣

∣

2

x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)

∣

∣

∣

∣

Hence, substituting the points (x

1

,y

1

)=(−4,1) ; (x

2

,y

2

)=(0,2) and (x

3

,y

3

)=(4,−3) in the area formula, we get

Area of given triangle =

∣

∣

∣

∣

2

(−4)(2+3)+(0)(−3−1)+4(1−2)

∣

∣

∣

∣

=

∣

∣

∣

2

−20+0−4

∣

∣

∣

=

2

24

=12 sq units

Answer 2

Answer:

17

Step-by-step explanation:

(-4 , -1) (1 , 2) (4 , -3)

Area of triangle =

                             $\frac{1}{2} [x_{1} (y_{2}-y_{3} )+x_{2}(y_{3}-y_{1} } ) +x_{3} (y_{1} -y_{2} )]\\\\\frac{1}{2} [-4(2-(-3))+1(-3-(-1))+4(-1-2)]\\\\\frac{1}{2} [-4(2+3)+1(-3+1)+4(-3)]\\\\\frac{1}{2} [-4(5)+1(-2)-12]\\\\\frac{1}{2} [-20-2-12]\\\\\frac{1}{2} [-34]\\\\-17$

Area of triangle can't be -ve

∴ Area of Triangle = 17