Find the value of x if the area of the triangle formed by (10, 2),(-3, -4),(x, 1), is 5

An example on how to find the value of x component of a triangle given the area and the two points.

$(10,2),(-3,-4),(x,1)\,$

The area of triangle is

$\frac{1}{2}|[10(-4-1)-3(1-2)+x(2+4)]|=5\,$

$\frac{1}{2}|-50+3+6x|=5\,$

$6x-47=10\,$

$x=\frac{57}{6}\,$

$x=\frac{19}{2}\,$

Therefore, the value of x is 19/2 units.

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