Question

Vertex%C2%A0 %C2%A0of rectangle%C2%A0 %C2%A0is located at%C2%A0 . A dilation of%C2%A0 %C2%A0will result in the image%C2%A0 . If the dilation is centered at the origin and has a scale factor of , what are the coordinates of%C2%A0 %C2%A0?

Answer 1

To determine the coordinates of a rectangle's vertex after dilation centered at the origin, you need the original coordinates of the vertex, the scale factor for the dilation, and then apply the dilation transformation.

1. **Understand the Dilation Formula**: If \((x, y)\) are the original coordinates of a point, and \(k\) is the scale factor, the new coordinates after dilation will be given by:
\[
(kx, ky)
\]

2. **Identify Original Coordinates and Scale Factor**: If you have the specific coordinates of the vertex (let's denote them as \((x_0, y_0)\)) and the scale factor \(k\), you plug them into the dilation formula.

3. **Calculate the New Coordinates**:
\[
\text{New coordinates} = (k \cdot x_0, k \cdot y_0)
\]

Please provide the original coordinates of the rectangle's vertex and the scale factor for further assistance in calculating the new coordinates.