1)Describe two mathematical graph transformations
2)Name types of congruences in maths when doing transformation
3)Determine the coordinates of C and D given that C is (4,1)
1) Two common mathematical graph transformations are translations and reflections.
- Translation: A translation is a transformation that shifts a graph horizontally or vertically. When translating a graph horizontally, each point on the graph is moved left or right by a certain amount. For example, if the graph of a function is translated 2 units to the right, every point on the graph will be shifted 2 units to the right. Similarly, when translating a graph vertically, each point is moved up or down by a certain amount.
- Reflection: A reflection is a transformation that "flips" a graph across a line. This line is called the line of reflection. Points on the graph that are on one side of the line of reflection are mapped to points on the other side of the line, while maintaining the same distance from the line. For example, a graph reflected across the x-axis would have all its points flipped vertically.
2) The types of congruences in math when doing transformations are:
- Congruent line segments: Two line segments are congruent if they have the same length. When a transformation is applied to a line segment, the resulting image will be congruent to the original segment if the transformation preserves length.
- Congruent angles: Two angles are congruent if they have the same measure. When a transformation is applied to an angle, the resulting image will be congruent to the original angle if the transformation preserves angle measures.
- Congruent triangles: Two triangles are congruent if their corresponding sides and angles are equal. When a transformation is applied to a triangle, the resulting image will be congruent to the original triangle if the transformation preserves side lengths and angle measures.
- Congruent shapes in general: Any two shapes are congruent if they have the same size and shape. Transformations can result in congruent shapes if they preserve distances, angles, and proportions.
3) To determine the coordinates of C and D given that C is (4, 1), we need more information, such as the nature of the transformation or the specific coordinates of D relative to C. The given point C alone does not provide enough information to determine the coordinates of D.