To understand the effect of the transformations on a triangle, let's break down the process:
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Translation (4 units right):
- When a triangle is translated 4 units to the right, every vertex of the triangle shifts 4 units in the positive x-direction. If the original triangle has vertices at \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\), after the translation, the new vertices will be \((x_1 + 4, y_1)\), \((x_2 + 4, y_2)\), and \((x_3 + 4, y_3)\).
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Reflection (over the x-axis):
- When a shape is reflected over the x-axis, the y-coordinates of its vertices are negated. If after the translation the triangle has vertices \((x_1 + 4, y_1)\), \((x_2 + 4, y_2)\), and \((x_3 + 4, y_3)\), reflecting these points over the x-axis results in the final vertices being \((x_1 + 4, -y_1)\), \((x_2 + 4, -y_2)\), and \((x_3 + 4, -y_3)\).
Summary:
The final image of the triangle, after being translated 4 units to the right and then reflected over the x-axis, will have the following characteristics:
- It retains the same shape and size as the original triangle.
- The triangle will be positioned in a way that it is flipped upside down compared to its original position due to the reflection.
- The x-coordinates of the vertices will all be increased by 4, while the y-coordinates will be inverted (sign changes).
This final image will be a triangle that is congruent to the original triangle but located in a different quadrant depending on the original positions of the vertices.