#modulus function

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Jedi: y = x

Sith: y = |x|

[maths-help]

Can you help me with this problem? Points A(0,3) and B(0, -3) are two verticies of triangle ABC. Write an equation or inequality that represents the set of all points C(x,y) that satisfy the given requirements. Find any restrictions for x. Triangle ABC is a right trangle. AB is not the longest side.

DIAGRAMS. DIAGRAMS ARE BRILLIANT FOR THIS KIND OF QUESTION.

Yours should look something like this:

After drawing in your points, you can figure out a few things. Since AB is not the hypotenuse, and ABC is a right triangle, C must lie on the line y=3 or the line y=-3.

You can write this as one equation by simply saying that the modulus of y is 3. (In this case, the modulus is essentially the magnitude; you ignore any minuses. You can notate the modulus of y by putting little lines on either side of it, as seen on the diagram.)

Then you need to look at your diagram again, and consider the x-values. Is there any x-value that lies on those lines that will not make a right triangle?

Yup. If x=0, it all overlaps, and you just get a line. Therefore, x is not equal to zero. Everywhere else on the line, however, will work.

So your final answer, representing the set of points that satisfy the requirements, is: mod (y) = 3 , x is not = to 0

For the proper notation, see the diagram.

-Margarita