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.