   SEARCH HOME Math Central Quandaries & Queries  Question from Sophia: For any point on line l, the product of the x-coordinate and the y-coordinate is less than or equal to zero , what is the answer? H Sophia,

Is l a particular line or you do this for any line?

Sophia write back

For any line

Sometimes when answering a math question it helps to experiment a little.

Suppose the line is the X-axis. Every point on the X-axis has coordinates $(x,0)$ for some real number $x$ so the product of the $x$ and $y$ coordinates is zero which satisfies "the product of the x-coordinate and the y-coordinate is less than or equal to zero".

Suppose the line is the Y-axis. Every point on the Y-axis has coordinates $(0,y)$ for some real number $y$ so the product of the $x$ and $y$ coordinates is zero which satisfies "the product of the x-coordinate and the y-coordinate is less than or equal to zero".

Now consider the lines $y = x$ and $y = -x.$ Take a few points on each of the lines and calculate the product of the $x$ and $y$ coordinates of each of the points you selected.

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