Question

if the area of the triangle formed by the points (x,4/3), (-2,6) and (3,1) is 5sq units ,then find the value of x

Answer 1

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Answer 2

Answer:  The required value of x is $\dfrac{14}{3},\dfrac{5}{3}.$

Step-by-step explanation:  Given that the area of the triangle formed by the vertices $\left(x,\frac{4}{3}\right),$ (-2, 6) and (3, 1) is 5 square units.

We are to find the value of x.

We know that

the area of a triangle formed by the vertices (a, b), (c, d) and (e, f) is given by

$A=|\dfrac{1}{2}\{a(d-f)+c(f-b)+e(b-d)\}|.$

So, according to the given information, we have

$5=|\dfrac{1}{2}\{x(6-1)-2(1-\frac{4}{3})+3(\frac{4}{3}-6)\}|\\\\\\\Rightarrow 5=|\dfrac{1}{2}(5x+\frac{2}{3}-14)|\\\\\\\Rightarrow 5=|\dfrac{1}{2}(5x-\frac{40}{3})|\\\\\\\Rightarrow 30=|6x-40|\\\\\Rightarrow 6x-40=30,~~~~6x-40=-30\\\\\Rightarrow 6x=70,~~~~\Rightarrow 6x=10\\\\\Rightarrow x=\dfrac{14}{3},\dfrac{5}{3}.$

Thus, the required value of x is $\dfrac{14}{3},\dfrac{5}{3}.$