Question

The area of the triangle with vertices (-1 2) (4 0) and (3 9) is

Answer 1

Solution;

Co-ordinates are :-

⇒( -1 , 2 ) , ( 4 , 0 ) and ( 3 , 9 )

The co-ordinates of the vertices of the given triangle are

$\rm \implies A=(x_1= -1 ,y_1=2) ,B=(x_2=4 , y_2=0)\: and \: C=(x_3=3 , y_3=9)$

Area of triangle( ΔABC)

$\rm=\dfrac{1}{2} |x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

$=\dfrac{1}{2} |-1(0-9)+4(9-2)+3(2-0)|$

$=\dfrac{1}{2} |-1(-9)+4(7)+3(2)|$

$=\dfrac{1}{2} |9+28+6|$

$=\dfrac{1}{2} \times43$

$\rm=21.5\:sq\:unit$

More formula related to this chapter

⇒ Distance formula

$\rm AB=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }$

⇒Section formula

$\rm x_1=\dfrac{mx_2+nx_1}{m+n} ,x_2=\dfrac{my_2+ny_1}{m+n}$