Question

Find the area of the triangle whose vertices are :(-4,6) (20,8) (9,10)​

Answer 1

Answer:

area of triangle = 35 sq units

Step-by-step explanation:

(-4,6) (20,8) (9,10)

x1 = -4. y1= 6

x2= 20. y2 =8

x3=9. y3= 10

using the formula to find area of triangle:

area of triangle = (1/2)| x1(y2-y3) + x2(y3-y1)+ x3(y1-y2)|

= (1/2) | -4(8-10) + 20(10-(6)) +9(6-8)|

= (1/2) | 8 + 80 -18|

= 70/2

=35

area of triangle = 35 sq units

Answer 2

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

$\green{\tt{\therefore{Area\:of\:triangle=35\:sq\:units}}}$

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

$\green{ \underline \bold{Given : }} \\ \tt{: \implies Coordinate \: of \: A= (-4,6) } \\ \\ \tt{: \implies Coordinate \: of \: B = (20,8) } \\ \\ \tt{: \implies Coordinate \: of \: C = (9,10) } \\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} | x_{1} ( y_{2} - y_{3}) + x_{2}( y_{3} - y_{1}) + x_{3}( y_{1} - y_{2} ) | } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |-4(8 - 10) + 20(10 - 6) + 9(6 - 8)| } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |-4 \times -2 + 20\times 4 + 9 \times -2 | } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} |8 + 80 -18| } \\ \\ \tt{: \implies Area \: of \: triangle = \frac{1}{2} \times 70} \\ \\ \green{\tt{: \implies Area \: of \: triangle =35 \: sq \: units}} \\ \\ \purple{\bold{Some \: formula \: related \: to \: coordinate \: geometery}} \\ \pink{\tt{ \circ \: Distance \: formula = \sqrt{ (x_{2} - x_{1})^{2} + ( y_{2} - y_{1} )^{2} } }} \\ \\ \pink{\tt{ \circ \: Section \: formula = x= \frac{m x_{2} + n x_{1} }{m + n} }}$