Question

find the area of triangle whose vertices are (4,3) (1,4) (2,3)​

Answer 1

Answer:

we know are of triangle

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

so solved the question with this formula

Answer 2

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

$\green{\tt{\therefore{Area\:of\:triangle=1\:sq\:units}}}$

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

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

• According to given question :

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