suppose you use the rule (3x+1,3y-4) to transform the original figure into a new figure. How would the side lengths of the new figure compare to the side lengths of the original? I need help fast. Thank you so much.
The homothetic factor is 3, so this is the ratio of the sides of the image compared to the original.
To determine how the side lengths of the new figure compare to the side lengths of the original figure, we need to understand how the rule (3x+1,3y-4) transforms points in the original figure.
In the given rule, the x-coordinate of each point is multiplied by 3 and then increased by 1, resulting in the new x-coordinate. Similarly, the y-coordinate of each point is multiplied by 3 and then decreased by 4, resulting in the new y-coordinate.
To compare the side lengths of the new figure to the original figure, we need to consider how these transformations affect the distances between points.
Let's consider a specific side in the original figure defined by two points: A(x1, y1) and B(x2, y2).
The distance between A and B in the original figure can be calculated using the distance formula:
d1 = √[(x2 - x1)^2 + (y2 - y1)^2]
Now, let's apply the rule to these two points to obtain their new coordinates:
A' (3x1 + 1, 3y1 - 4) and B' (3x2 + 1, 3y2 - 4)
Using the distance formula again, we can calculate the distance between A' and B':
d2 = √[(3x2 + 1 - 3x1 - 1)^2 + (3y2 - 4 - 3y1 + 4)^2]
By simplifying this expression, we can compare d1 and d2 to determine the relationship between the side lengths of the original and new figure.
Repeat this process for all the sides of the original figure to analyze how the side lengths are affected by the given rule.