suppose you use the rule (3x+1,3y-4) to transform the original figure into a new figure. How would the angles of the new figure compare with the angles of the original? Please, I need help ASAP
The transformation is isotropic, i.e. expands/contracts in the same proportion in both directions, evidenced by the common factor 3 in both x and y.
Thus the image retains the same shape as the original, in other words, angles are preserved.
The +1 and -4 are translations which do not change the shape nor the size of the image.
To determine how the angles of the new figure compare to the angles of the original figure after applying the given rule, you can follow these steps:
1. Understand the given rule: The rule (3x + 1, 3y - 4) represents a transformation that applies a linear function to each point (x, y) of the original figure. The function multiplies the x-coordinate by 3 and adds 1, while multiplying the y-coordinate by 3 and subtracting 4.
2. Recall the properties of linear transformations: Linear transformations, such as the one described in the given rule, preserve parallel lines, ratios of lengths, and straight angles (180 degrees). However, they do not necessarily preserve the measures of angles other than straight angles.
3. Analyze the effects on angles: Applying the transformation to each point of the original figure affects the position of the points but does not change the shape nor the relative orientation of the figure. Therefore, the transformation will not alter the relationships between angles in terms of which angles are complementary, supplementary, or congruent to each other.
4. Determine the effects on angle measures: Since the transformation does not change the shape or orientation of the original figure, the measures of angles in the new figure will be equal to the measures of the corresponding angles in the original figure. In other words, if a pair of angles in the original figure is congruent, then the corresponding pair in the new figure will also be congruent.
Therefore, the angles of the new figure will have the same measures as the angles of the original figure. The transformation rule (3x + 1, 3y - 4) does not affect the measures of angles in the figure, only their positions in space.