Find the coordinates of the vertices of the figures formed by y -< x + 2, x + 2 -< 6, and y >- -2
A)(0,0),(2,4),(8,-2)
B)(-4,-2),(2,4),(8,-2)
C)(-4,-2),(4,2),(8,-2)
D)(-2,-4),(2,4),(8,-2)
I chose B
this one confused me this is all the work to show:
-2 -< -4 + 2
2 + 4 -< 6
-2
3 answers
the way u did it, if I try to do the others, Aren't they all true though?
No, all are not true
We have this:
(y -< x + 2) = point 1.
(x + 2 -< 6) = point 2.
(y >- -2) = point 3.
Replace all inequality symbols with an equal sign for easy simplification.
Point 3:
y >- -2 becomes y = -2
We just found y.
We plug y = -2 in point 1 to find x.
-2 = x + 2
-2 - 2 = x
-4 = x
We know that y = -2 and x = -4.
================================
Notice that the next point to follow in choice B is (2,4), where x = 2 and y = 4.
We plug that into all three points to see if we get a true statement.
(y -< x + 2) = point 1.
4 -< 2 + 2...true statement
(x + 2 -< 6) = point 2.
2 + 4 -< 6...true statement
(y >- -2) = point 3.
4 >- -2...true statement
So far, it appears that choice B is correct.
===================================
What is the next point given in choice B? It is point (8, -2).
We do the same-->plug to check for true statement.
(y -< x + 2) = point 1.
-2 -< 8 + 2...true statement
(x + 2 -< 6) = point 2.
8 + 2 -< 6...false statement
(y >- -2) = point 3.
-2 >- -2...true statement
We know that choice A and D cannot be the answers. We just found out that choice B is most likely not the answer because of the false statement.
I would say the answer is choice C.
(y -< x + 2) = point 1.
(x + 2 -< 6) = point 2.
(y >- -2) = point 3.
Replace all inequality symbols with an equal sign for easy simplification.
Point 3:
y >- -2 becomes y = -2
We just found y.
We plug y = -2 in point 1 to find x.
-2 = x + 2
-2 - 2 = x
-4 = x
We know that y = -2 and x = -4.
================================
Notice that the next point to follow in choice B is (2,4), where x = 2 and y = 4.
We plug that into all three points to see if we get a true statement.
(y -< x + 2) = point 1.
4 -< 2 + 2...true statement
(x + 2 -< 6) = point 2.
2 + 4 -< 6...true statement
(y >- -2) = point 3.
4 >- -2...true statement
So far, it appears that choice B is correct.
===================================
What is the next point given in choice B? It is point (8, -2).
We do the same-->plug to check for true statement.
(y -< x + 2) = point 1.
-2 -< 8 + 2...true statement
(x + 2 -< 6) = point 2.
8 + 2 -< 6...false statement
(y >- -2) = point 3.
-2 >- -2...true statement
We know that choice A and D cannot be the answers. We just found out that choice B is most likely not the answer because of the false statement.
I would say the answer is choice C.