The coordinates of the quadrilateral, VWXY are given below. Find the coordinates of its image after dilation with a given scale factor.
To find the coordinates of the image after dilation, we need the scale factor and the coordinates of the original quadrilateral.
Let's first understand what a dilation is. A dilation is a transformation that resizes an object without changing its shape. It involves multiplying the coordinates of each point by a scale factor.
Here are the steps to find the coordinates of the image after dilation:
1. Start with the coordinates of the original quadrilateral: V(x1, y1), W(x2, y2), X(x3, y3), and Y(x4, y4).
2. Determine the scale factor, which specifies how much the quadrilateral will be stretched or shrunk. Let's denote the scale factor as 'k'.
3. Apply the dilation formula to each coordinate:
- New x-coordinate = k * x-coordinate
- New y-coordinate = k * y-coordinate
4. Substitute the values of the original coordinates and the scale factor into the formulas to find the new coordinates.
Let's go through an example using specific values:
Original coordinates: V(2, 3), W(4, 6), X(7, 5), Y(9, 1)
Scale factor: k = 2
Apply the dilation formula:
New coordinates:
V' = (k * x1, k * y1) = (2 * 2, 2 * 3) = (4, 6)
W' = (k * x2, k * y2) = (2 * 4, 2 * 6) = (8, 12)
X' = (k * x3, k * y3) = (2 * 7, 2 * 5) = (14, 10)
Y' = (k * x4, k * y4) = (2 * 9, 2 * 1) = (18, 2)
Therefore, the coordinates of the image after a dilation with a scale factor of 2 are:
V'(4, 6), W'(8, 12), X'(14, 10), Y'(18, 2).