1. The problem involves identifying and understanding points on the Cartesian plane, including their coordinates and quadrant positions. 2. The Cartesian plane consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). The origin is the point where these axes intersect, at coordinates $(0,0)$. 3. The plane is divided into four quadrants: - Quadrant I: $x>0$, $y>0$ - Quadrant II: $x<0$, $y>0$ - Quadrant III: $x<0$, $y<0$ - Quadrant IV: $x>0$, $y<0$ 4. Given points: - Point A is in Quadrant IV with $y=3$, so coordinates are $(x,3)$ with $x>0$. - Point D is given as $(0,6)$ on the y-axis. - Point C is in Quadrant II with $y=3$, so coordinates are $(-x,3)$ with $x>0$. - Point E is on the x-axis at $(3,0)$. 5. Explanation: - Point D lies on the y-axis, so its $x$-coordinate is 0. - Point E lies on the x-axis, so its $y$-coordinate is 0. - Points in Quadrant IV have positive $x$ and negative $y$, but since $y=3$ is positive, Point A must be in Quadrant I or IV with $y=3$; given the problem states IV quadrant, $y$ should be negative, so likely a typo or Point A is at $(x,-3)$. - Point C in Quadrant II has negative $x$ and positive $y=3$. 6. Summary of coordinates: - Point A: $(x,-3)$ with $x>0$ (Quadrant IV) - Point D: $(0,6)$ (y-axis) - Point C: $(-x,3)$ with $x>0$ (Quadrant II) - Point E: $(3,0)$ (x-axis) 7. Rene Descartes introduced this coordinate system, allowing algebraic representation of geometric points. Final answers: - Point A: $(?, -3)$ in Quadrant IV - Point D: $(0,6)$ on y-axis - Point C: $(-?,3)$ in Quadrant II - Point E: $(3,0)$ on x-axis