The present invention extends to methods, systems, and computer program products for recognizing multiple input point gestures. A recognition module receives an ordered set of points indicating that contacts have been detected in a specified order at multiple different locations on a multi-touch input surface. The recognition module determines the position of subsequently detected locations (e.g., third detected location) relative to (e.g., to the left of right of) line segments connecting previously detected locations (e.g., connecting first and second detected locations). The gesture module also detects whether line segments connecting subsequently detected locations (e.g., connecting third and fourth detected locations) intersect line segments connecting previously detected locations (e.g., connecting first and second detected locations). The gesture module recognizes an input gesture based on the relative positions and whether or not line segments intersect. The gesture module then identifies a corresponding input operation (e.g., cut, paste, etc.) to be performed.