If the area of the triangle formed by the points $(x, 2 x), (- 2, 6)$ and $(3, 1)$ is $5$ square units , then $x$
(a) $23$
(b) $35$
(c) $3$
(d) $5$

Question

If the area of the triangle formed by the points -2-3- -4-5- and -3-y- is 10 square then y -dfrac-19-3-dfrac-21-3-dfrac-23-3-dfrac-25-3-

Toppr Admin · Accepted Answer

Area of triangle having vertices -x1-y1-x2-y2- and -x3-y3- is given by-xA0-12-xD7-x1-y2-x2212-y3-x2-y3-x2212-y1-x3-y1-x2212-y2-Area-12-x2212-2-x2212-5-x2212-y-4-y-x2212-3-x2212-3-3-5-xA0- -xA0- -xA0- -xA0- -xA0- -12-10-2y-4y-x2212-12-x2212-24-xA0- -xA0- -xA0- -xA0- -xA0- -12-6y-x2212-26-3y-x2212-133y-x2212-13-10-xA0-sq-unit-xA0-y-233

If the area of the triangle formed by the points (−2,3),(4,−5) and (−3,y) is 10 square units then y=193213233253

Area of triangle having vertices (x1,y1),(x2,y2) and (x3,y3) is given by =12×[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]Area=12[−2(−5−y)+4(y−3)−3(3+5)] =12(10+2y+4y−12−24) =12(6y−26)=3y−133y−13=10 sq.unit y=233

If the area of the triangle formed by the points $(- 2, 3), (4, - 5)$ and $(- 3, y)$ is 10 square units then $y =$
$\frac{19}{3}$
$\frac{21}{3}$
$\frac{23}{3}$
$\frac{25}{3}$