Question

find the area of triangle whose vertices are 10,6 , 2,5, -1,3​

Answer 1

Answer:

Use determinant of a matrix formula to calculate area of the triangle.

Step-by-step explanation:

Based on the counterclockwise entry of the coordinates of the vertices of the triangle (x1, y1), (x2, y2), (x3, y3) or (10, 6), (2, 5), (-1, 3): A = (x1y2 + x2y3 + x3y1 – x1y3 – x2y1 – x3y2)/2.

Answer 2

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

$\green{\tt{\therefore{Area\:of\:triangle=6.5\:sq\:units}}}$

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

$\green{ \underline \bold{Given : }} \\ \tt{: \implies Coordinate \: of \: A= (10,6) } \\ \\ \tt{: \implies Coordinate \: of \: B = (2,5) } \\ \\ \tt{: \implies Coordinate \: of \: C = (-1,3) } \\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} | x_{1} ( y_{2} - y_{3}) + x_{2}( y_{3} - y_{1}) + x_{3}( y_{1} - y_{2} ) | } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |10(5 - 3) + 2(3 - 6) + (-1)(6 - 5)| } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |10 \times 2 + 2\times - 3 - 1 \times 1 | } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |20 - 6 - 1| } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} \times 13} \\ \\ \green{\tt{: \implies Area \: of \: triangle =6.5 \: sq \: units}} \\ \\ \purple{\bold{Some \: formula \: related \: to \: coordinate \: geometery}} \\ \pink{\tt{ \circ \: Distance \: formula = \sqrt{ (x_{2} - x_{1})^{2} + ( y_{2} - y_{1} )^{2} } }} \\ \\ \pink{\tt{ \circ \: Section \: formula = x= \frac{m x_{2} + n x_{1} }{m + n} }}$