suppose hector dilates the rectangle shown below with the center of dilation at 0,0 and a scale factor of 2 and then translates the figure 1 unit to the left. what will be the coordinates the vertices of the similar figure that results, One point on figure is -3,2
To find the coordinates of the vertices of the similar figure that results from the dilation and translation, we will follow these steps:
1. Apply the dilation with a scale factor of 2: Multiply the x and y coordinates of each vertex by 2.
- Original point: (-3, 2)
- Dilation: (-3 * 2, 2 * 2) = (-6, 4)
2. Apply the translation of 1 unit to the left: Subtract 1 from the x coordinate of each vertex.
- Translated point: (-6 - 1, 4) = (-7, 4)
Therefore, the coordinate of the vertex after the dilation and translation is (-7, 4).
To find the coordinates of the vertices of the similar figure, we need to follow the steps of the transformations as described:
1. Dilation with a scale factor of 2:
To dilate a point with respect to the origin, we multiply its coordinates by the scale factor. Let's consider the given point (-3, 2). When we apply the dilation with a scale factor of 2, we get the new coordinates: (-3 * 2, 2 * 2) = (-6, 4).
2. Translation 1 unit to the left:
To translate a point, we add or subtract a certain amount from its coordinates. In this case, we need to move the point 1 unit to the left. So, we subtract 1 from the x-coordinate. The new coordinates become: (-6 - 1, 4) = (-7, 4).
Therefore, after the given transformations, the coordinates of the similar figure's vertex that started at (-3, 2) become (-7, 4).