coordinate-figure-computation
A polygon or other figure is given by coordinates; the task is to compute an unknown coordinate, length, or area. The structural move is reading off horizontal/vertical distances directly from coordinate differences, then applying a one-line geometric formula (base × height / 2, etc).
풀이 전략
- Keep base axis-aligned but rotate the apex location (e.g. unknown x instead of unknown y) — symmetric variant
- Change figure_type to parallelogram so base × height is still the formula
- For a harder variant, tilt the base so the height must be derived from the perpendicular distance formula
세부 유형 분포 (6)
한 줄을 클릭하면 그 안의 문제를 볼 수 있어요.
- axis-aligned-area-formula 19% (5)
The figure has at least one axis-parallel base; read base and height directly from coordinate differences and apply a single closed-form formula (base × height, base × height / 2, or diagonal1 × diagonal2 / 2) to find the area or, in reverse, to solve for one unknown coordinate or dimension.
- pythagorean-distance-length 23% (6)
A segment length, radius, or diagonal inside a coordinate figure is unknown; form a right triangle whose legs are axis-aligned coordinate differences, then apply the Pythagorean theorem (or distance formula) to compute the target length directly.
- shoelace-polygon-area 23% (6)
The polygon's vertices are non-axis-aligned lattice points; compute the area by the shoelace formula, the bounding-box-minus-corner-triangles method, or Pick's theorem, then use the result to answer a comparison or ratio question.
- line-intersection-area 12% (3)
Two or more lines are given by explicit equations or slopes; find the vertices of the enclosed region by solving the pairwise intersection systems, then compute the polygon's area (or count intersection points with a boundary) using the identified vertices.
- coordinate-graph-slope-interpretation 12% (3)
A plotted point or curve sits on a coordinate graph where the axes represent two real-world quantities; the key insight is that the ratio y/x (slope of the line from the origin to the point) equals a rate such as speed or price-per-unit, so the optimal or target value corresponds to the flattest or steepest such line, or the relevant time intervals are read directly off the curve.
- coordinate-figure-constraint 12% (3)
A geometric figure's dimensions or a point's coordinates are governed by one or more constraint equations (angle sums, dimension-addition identities, or transformation rules); set up the system from the figure's structure and solve it algebraically to recover the target unknown.
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