Question

find the area of triangle whose vertices are ( -3,4 ),( 7,8 ),( 5,6 )

Answer 1

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

$\green{\tt{\therefore{Area\:of\:triangle=6\:sq\:units}}}$

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

$\green{ \underline \bold{Given : }} \\ \tt{: \implies Coordinate \: of \: A= (-3,4) } \\ \\ \tt{: \implies Coordinate \: of \: B = (7,8) } \\ \\ \tt{: \implies Coordinate \: of \: C = (5,6) } \\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} | x_{1} ( y_{2} - y_{3}) + x_{2}( y_{3} - y_{1}) + x_{3}( y_{1} - y_{2} ) | } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |-3(8 - 6) + 7(6- 4) + 5(4 - 8)| } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |-3 \times 2 + 7\times 2 + 5 \times -4 | } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |-6 + 14 -20| } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} \times 12} \\ \\ \green{\tt{: \implies Area \: of \: triangle =6 \: sq \: units}} \\ \\ \purple{\bold{Some \: formula \: related \: to \: coordinate \: geometery}} \\ \pink{\tt{ \circ \: Distance \: formula = \sqrt{ (x_{2} - x_{1})^{2} + ( y_{2} - y_{1} )^{2} } }} \\ \\ \pink{\tt{ \circ \: Section \: formula = x= \frac{m x_{2} + n x_{1} }{m + n} }}$