quadrilateral PQRS was dilated to produce quadrilateral PQRS on the grid below.
Oh, I see! It's like Quadrilateral PQRS went to the gym and got all stretched out. Or maybe it went to the spa and got a fantastic makeover. Anyway, I hope Quadrilateral PQRS is feeling fabulous after its dilation!
To understand how quadrilateral PQRS was dilated, we would need more specific information about the grid and the scale factor used. Dilations involve scaling the size of the original shape by a certain factor, so knowing the scale factor is crucial.
However, I can still explain the general concept of dilating a quadrilateral on a grid. In a dilation, each point of the original quadrilateral is moved along a line that passes through the center of dilation. The distance between each point and the center of dilation is scaled by the scale factor.
To determine the new coordinates of the dilated quadrilateral PQRS, you can follow these steps:
1. Label the coordinates of the original quadrilateral PQRS as (x1, y1), (x2, y2), (x3, y3), and (x4, y4), respectively.
2. Identify the center of dilation. This point is often referred to as the origin (0, 0) on the grid.
3. Determine the scale factor. If you have the scale factor, multiply the distance between each point and the center of dilation by that factor.
4. Calculate the new coordinates. Use the scale factor to calculate the new coordinates of each point using the following formulas:
- New x-coordinate = scale factor * (original x-coordinate - x-coordinate of the center of dilation)
- New y-coordinate = scale factor * (original y-coordinate - y-coordinate of the center of dilation)
5. Plug in your values and calculate the new coordinates for each point, P', Q', R', and S', of the dilated quadrilateral.
Without specific values for the scale factor and the original coordinates of PQRS, we cannot provide the exact new coordinates of PQRS'. However, by following the steps above, you should be able to find the new coordinates once you have the necessary information.