Question

Find the area of the triangle whose vertices are 4,3 -1,0and2,-4

Answer 1

the given vertices are (4,3) ,(-1,0),(2,-4)
then the distance between any two points gives the length (or breadth)
the distance between one of the two points used above and the another point gives the breadth (or length)

therefore the answer is 30 sq.units

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Area\:of\:triangle=14.5\:sq\:units}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ \tt{: \implies Coordinate \: of \: A= (4,3) } \\ \\ \tt{: \implies Coordinate \: of \: B = (-1,0) } \\ \\ \tt{: \implies Coordinate \: of \: C = (2,-4) } \\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} | x_{1} ( y_{2} - y_{3}) + x_{2}( y_{3} - y_{1}) + x_{3}( y_{1} - y_{2} ) | } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |4(0 -(-4)) -1(-4 -3) + 2(3 - 0)| } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |4 \times 4 - 1\times -7 + 2 \times 3 | } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |16+ 7 +6| } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} \times 29} \\ \\ \green{\tt{: \implies Area \: of \: triangle =14.5 \: sq \: units}} \\ \\ \purple{\bold{Some \: formula \: related \: to \: coordinate \: geometery}} \\ \pink{\tt{ \circ \: Distance \: formula = \sqrt{ (x_{2} - x_{1})^{2} + ( y_{2} - y_{1} )^{2} } }} \\ \\ \pink{\tt{ \circ \: Section \: formula = x= \frac{m x_{2} + n x_{1} }{m + n} }}$