1. The problem asks to find dots on a grid to form a quadrilateral with one of these properties: a perpendicular bisector forming a right angle, equal sides, or no parallel sides. 2. To solve this, recall that: - A perpendicular bisector of a segment is a line that divides it into two equal parts at a right angle. - A quadrilateral with equal sides is a rhombus or square. - A quadrilateral with no parallel sides is called a general irregular quadrilateral. 3. Step 1: Identify four dots that form a quadrilateral. 4. Step 2: Check if any two sides are equal in length by calculating distances between points using the distance formula $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$. 5. Step 3: Check if any side has a perpendicular bisector by verifying if the midpoint of a side is equidistant from the endpoints and if the adjacent sides meet at a right angle (90 degrees). Use the slope formula $$m=\frac{y_2-y_1}{x_2-x_1}$$ and check if the product of slopes of adjacent sides is $$-1$$. 6. Step 4: To find a quadrilateral with no parallel sides, ensure no two sides have equal slopes. 7. For part (b), to form a regular polygon with more than 3 sides on a dotted grid, select dots equally spaced around a center point so that all sides and angles are equal. 8. For example, a regular hexagon can be formed by choosing six dots equally spaced in a circular pattern. Final answer: By applying these steps, you can identify the required quadrilaterals and regular polygons on the given grids.