sandy wrote:
In the xy-plane, one of the vertices of square S is the point (2, 2). The diagonals of S intersect at the point (6, 6).
Quantity A |
Quantity B |
Area of S |
64 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Since the diagonals of S intersect at the point (6, 6), we can say that (6,6) is the CENTER of the square.
Notice that, to get from point (2,2) to the CENTER at (6,6), we must travel up 4 units and then travel to the right 4 units.

Since (6,6) is the CENTER of the square, we can find another vertex by starting at the center and travelling 4 units up and then 4 units to the right

Now that we have our second vertex, we can see that the entire square looks like this:

Since each side of the square has length 8, the area of the square = (8)(8) = 64
We get:
QUANTITY A: 64
QUANTITY B: 64
Answer: C
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep