How to find the area using graph points?

60 Views Asked by At

Graph pic

In this graph , there are eight areas namely A,B,C,D,E,F,G and H.

How to find the area using graph points ?

For example :

(20,50) this point is in the area A so , the answer is A.

Is There any formula for finding the area using graph points ?

How can I find the area using graph points?

1

There are 1 best solutions below

1
On BEST ANSWER

Like Jaap Scherphuis mentioned in a comment, construct a truth table: $$\begin{array}{c|c|c|c} x \gt 0 & y \gt 0 & \lvert x \rvert \gt 2 \lvert y \rvert & \lvert y \rvert \gt 2 \lvert x \rvert & \text{Region} \\ \hline \text{No} & \text{No} & \text{No} & \text{No} & \text{F} \\ \text{No} & \text{No} & \text{No} & \text{Yes} & \text{E} \\ \text{No} & \text{No} & \text{Yes} & \text{No} & \text{G} \\ \text{No} & \text{No} & \text{Yes} & \text{Yes} & \text{!} \\ \text{No} & \text{Yes} & \text{No} & \text{No} & \text{H} \\ \text{No} & \text{Yes} & \text{No} & \text{Yes} & \text{A} \\ \text{No} & \text{Yes} & \text{Yes} & \text{No} & \text{G} \\ \text{No} & \text{Yes} & \text{Yes} & \text{Yes} & \text{!} \\ \text{Yes} & \text{No} & \text{No} & \text{No} & \text{D} \\ \text{Yes} & \text{No} & \text{No} & \text{Yes} & \text{E} \\ \text{Yes} & \text{No} & \text{Yes} & \text{No} & \text{C} \\ \text{Yes} & \text{No} & \text{Yes} & \text{Yes} & \text{!} \\ \text{Yes} & \text{Yes} & \text{No} & \text{No} & \text{B} \\ \text{Yes} & \text{Yes} & \text{No} & \text{Yes} & \text{A} \\ \text{Yes} & \text{Yes} & \text{Yes} & \text{No} & \text{C} \\ \text{Yes} & \text{Yes} & \text{Yes} & \text{Yes} & \text{!} \\ \end{array}$$ Note that both $\lvert x \rvert \gt 2 \lvert y \rvert$ and $\lvert y \rvert \gt 2 \lvert x \rvert$ cannot be true at the same time; these are marked with a $\text{!}$ in the region, denoting "impossible".

Also note that a point is within the specified square if and only if $\lvert x \rvert \le 50$ and $\lvert y \rvert \le 50$.


Note that the above also includes the origin ($x = 0$, $y = 0$) in region $\text{F}$, and the separation lines $y = \pm 2 x$ and $x = \pm 2 y$ in their respective regions. Depending on which regions you wish these to belong to, you may want to change some of the rules from $\gt$ to $\ge$, or even add extra checks ($x = 0$, $y = 0$, $x = 2 y$, $x = -2 y$, $y = 2 x$, $y = - 2 x$).