If two curves touch at a point and do not cross, the mathematical term for the point is

If two curves touch at a point and do not cross, the mathematical term for the point is

• A. Tangency
• B. Intersection
• C. Confluence
• D. Vertex

Answer: (A)

Touching without crossing is called tangency. At a tangency point, the two curves share a common tangent line, and their slopes are the same there, so locally they travel in the same direction as they meet. Because of that shared tangent, the curves meet without crossing each other. The term “point of tangency” describes the exact location where this happens. In contrast, a general intersection just means the curves meet, which can involve crossing. A vertex is a sharp corner, and confluence isn’t used in this context. For example, y = x^2 and y = 0 touch at (0,0) since the slope of x^2 is 0 there, matching the tangent of the x-axis, and the parabola stays on one side of the axis near that point.

Touching without crossing is called tangency. At a tangency point, the two curves share a common tangent line, and their slopes are the same there, so locally they travel in the same direction as they meet. Because of that shared tangent, the curves meet without crossing each other. The term “point of tangency” describes the exact location where this happens. In contrast, a general intersection just means the curves meet, which can involve crossing. A vertex is a sharp corner, and confluence isn’t used in this context. For example, y = x^2 and y = 0 touch at (0,0) since the slope of x^2 is 0 there, matching the tangent of the x-axis, and the parabola stays on one side of the axis near that point.