Math Snap

STEP 1

Assumptions1. The statement is "If the product of a point's coordinates is positive, the point must be in quadrant I."
. The quadrants of the Cartesian coordinate system are numbered as follows Quadrant I (positive x, positive y), Quadrant II (negative x, positive y), Quadrant III (negative x, negative y), and Quadrant IV (positive x, negative y).
3. The product of a point's coordinates is found by multiplying the x-coordinate by the y-coordinate.

STEP 2

Let's analyze the statement. If the product of a point's coordinates is positive, this means that both coordinates are either positive or both are negative.

STEP 3

In the Cartesian coordinate system, both coordinates are positive in Quadrant I and both are negative in Quadrant III. Therefore, if the product of a point's coordinates is positive, the point could be in either Quadrant I or Quadrant III.

STEP 4

Comparing the result from3 with the original statement, we can see that the original statement is false because it does not include the possibility of the point being in Quadrant III.

STEP 5

Now, let's look at the provided options to find the correct statement.

STEP 6

Option A is incorrect because the point could not be in Quadrant IV if the product of its coordinates is positive.

STEP 7

Option B is incorrect because the point could not be in Quadrant II if the product of its coordinates is positive.

STEP 8

Option C is correct because it matches our finding in3 that the point could be in either Quadrant I or Quadrant III if the product of its coordinates is positive.

Option D is incorrect because the original statement is false, as we determined in4.
The correct answer is C. The statement is false. The true statement is, if the product of a point's coordinates is positive, the point must be in quadrant I or quadrant III.