The statement that would result in figure ABCD being completely in quadrant four is when all the x-coordinates of the vertices of the figure are positive, and all the y-coordinates are positive.
To determine if figure ABCD is completely in quadrant four, we need to understand the relationship between the coordinates of the vertices of the figure and the quadrants on the coordinate plane.
In quadrant four, both the x-coordinate and the y-coordinate of a point are positive. Therefore, for figure ABCD to be completely in quadrant four, all the vertices of the figure must have positive x-coordinates and positive y-coordinates.
Let's look at some statements to see if they would result in figure ABCD being completely in quadrant four:
1. Statement: All the x-coordinates of the vertices of figure ABCD are positive, and all the y-coordinates are negative.
Explanation: If all the x-coordinates are positive and all the y-coordinates are negative, figure ABCD would not be in quadrant four because quadrant four requires both x and y coordinates to be positive.
2. Statement: All the x-coordinates of the vertices of figure ABCD are negative, and all the y-coordinates are positive.
Explanation: If all the x-coordinates are negative and all the y-coordinates are positive, figure ABCD would not be in quadrant four because quadrant four requires both x and y coordinates to be positive.
3. Statement: All the x-coordinates of the vertices of figure ABCD are positive, and all the y-coordinates are positive.
Explanation: If all the x-coordinates are positive and all the y-coordinates are positive, figure ABCD would be completely in quadrant four because both the x and y coordinates are positive.