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Explain Bot To take triangle ABC onto triangle A'B'C, you need to apply a combination of translations, rotations, reflections, and/or dilations.
1. Translation: If triangle A'B'C is obtained by shifting triangle ABC horizontally or vertically, you just need to add the same values to the corresponding coordinates of each vertex of triangle ABC.
2. Rotation: If triangle A'B'C is obtained by rotating triangle ABC about a certain point, you need to determine the angle of rotation and the center of rotation. Then, use the rotation formulas to find the new coordinates of each vertex.
3. Reflection: If triangle A'B'C is obtained by reflecting triangle ABC over a certain line (e.g., a vertical or horizontal line), you need to find the equation of that line. Then, use the reflection formulas to find the new coordinates.
4. Dilation: If triangle A'B'C is obtained by enlarging or reducing triangle ABC, you need to find the scale factor and the center of dilation. Then, multiply the coordinates of each vertex by the scale factor.
By carefully analyzing the given triangles and considering the possible transformations, you can identify which transformation(s) are needed and determine the specific values required to map triangle ABC onto triangle A'B'C.