the rul (x,3/4y) is applied to a polygon. Is the image similar to the original polygon?
To determine if the image obtained by applying the rule (x, 3/4y) to a polygon is similar to the original polygon, we need to understand what the rule does to the polygon.
The rule (x, 3/4y) means that for each point (x, y) in the original polygon, the image point will be at coordinates (x, 3/4y). This means that the x-coordinate remains the same, but the y-coordinate is scaled down by a factor of 3/4.
To decide if the image is similar to the original polygon, we need to check if the corresponding sides of the two polygons are proportional and if the corresponding angles are equal.
1. Proportional sides:
For two polygons to be similar, their corresponding sides must be proportional. To check this, compare the lengths of the corresponding sides in the original and image polygons. If the ratios of corresponding side lengths are the same or equal, then the sides are proportional.
2. Equal angles:
For two polygons to be similar, their corresponding angles must be equal. To check this, compare the measures of the corresponding angles in the original and image polygons. If the angles are the same or equal, then the angles are equal.
By verifying the proportions of the corresponding sides and the equality of the corresponding angles, you can determine if the image obtained by applying the rule (x, 3/4y) is similar to the original polygon.
To determine if the image is similar to the original polygon, we need to compare the corresponding side lengths of both figures.
The rule (x, 3/4y) means that for each point (x, y) in the original polygon, the corresponding point in the image will be (x, 3/4y). This means that the x-coordinate remains the same, but the y-coordinate is multiplied by 3/4.
Since only the y-coordinate changes, the horizontal distances between points remain the same in both figures. However, the vertical distances are reduced by a scale factor of 3/4.
Therefore, the image is similar to the original polygon, but it is smaller in size.