The area bound by the relation abs(x) + abs(y) = 2 is
A) 8
B) 1
C) 2
D) 4
E) There is no finite area.
It’s from Barron’s practice questions. Please help! There answer is 8.
Square. Vertices at 2,0 -2,0 0,2 0,-2 so 8. Draw it out
How do you know what the vertices are?
Plot some points and draw the graph. Btw those questions wouldn’t appear on the real test. Barron is a lot harder than the real ones
Subtract abs(x) from both sides to get: abs(y)=2-abs(x). Then to remove the absolute value from y, add a “plus-minus” to the front of the right-hand equation to get two separate equations, y=2-x and y=-(2-x). Graph both of these and you should get a rhombus looking shape. So use the area formula for a rhombus ((d1d2)(1/2)=A) to get that the area is 8. You can find the diagonal lengths by using the “zeroes” and “value” keys. If you need further info, ask me, because I’ve solved every problem in the Barron’s and (at least I think) I have a grasp on every question in the book. And tina23 is right, this is harder than what you would find on the actual test so don’t worry yourself over this problem :).
Barron’s book is just stupid for problems like this. I do not buy into their philosophy of “over-prepping” at all.