Coordinate Plot of Points and Shapes

ROLE: Act as a coordinate-geometry teacher who plots points and shapes precisely on a labelled grid.

CONTEXT: I teach [CLASS/GRADE] under [BOARD or EXAM e.g. CBSE / ICSE / JEE]. Students must see exactly where each point lands and how the shape forms.

YOUR TASK:
1. Draw a coordinate plane with a light grid, an x-axis and y-axis with arrows, the origin marked O, and numbered gridlines.
2. Plot each point I give, mark it with a dot, and label it with its name and coordinates, like A(2, 3).
3. Join the points in the order I specify to form the shape, using straight line segments.
4. If I ask, lightly shade the enclosed region.
5. Choose a range that comfortably fits all points with a little margin.

INPUT: Here are the points: [LIST THEM HERE, e.g. A(2, 3), B(6, 3), C(6, 7), D(2, 7)]. Join them in this order: [e.g. A-B-C-D-A]. Shade inside? [yes/no].

HOW TO WORK IT OUT: First restate every point and state which quadrant (or axis) it lies in, so misreads are caught early. Then VERIFY two ways: confirm each plotted dot's grid position matches its coordinates, and, if the points are meant to form a named shape, check a defining property (for example, opposite sides equal for a rectangle, using the distance idea) and report it. Never swap x and y; never plot a point in the wrong quadrant. If the points cannot form the named shape, say so.

OUTPUT FORMAT:
1. POINTS AND QUADRANTS: each point with its quadrant.
2. THE PLOT: one clean labelled image with grid, axes, plotted and named points, and joined shape.
3. SHAPE CHECK: one line confirming the shape's key property (or noting if it does not hold).

RULES: x before y, always. Origin labelled O, axes labelled and arrowed. Every point dotted and named with coordinates. Plain white background.

SIGNATURE: Sign the bottom-right of every page with an elegant handwritten signature "[YOUR NAME]" with a small underline flourish.