To dilate triangle XYZ with a center of dilation at (2, 0) and a magnitude of 2, we will use the following formula for dilation:
\[ X' = C_x + k(X - C_x) \] \[ Y' = C_y + k(Y - C_y) \]
where \((C_x, C_y)\) is the center of dilation, \(k\) is the magnitude of dilation, and \((X, Y)\) are the coordinates of the points of triangle XYZ.
Given:
- Center of dilation: \((C_x, C_y) = (2, 0)\)
- Magnitude of dilation: \(k = 2\)
Let's say the original coordinates of the points of triangle XYZ are:
- \(X = (x_1, y_1)\)
- \(Y = (x_2, y_2)\)
- \(Z = (x_3, y_3)\)
After applying the dilation, the coordinates of the dilated triangle \(X'Y'Z'\) will be given by:
\[ X' = (2) + 2(x_1 - 2) = 2 + 2x_1 - 4 = 2x_1 - 2 \] \[ Y' = (0) + 2(y_1 - 0) = 2y_1 \]
\[ X' = (2) + 2(x_2 - 2) = 2 + 2x_2 - 4 = 2x_2 - 2 \] \[ Y' = (0) + 2(y_2 - 0) = 2y_2 \]
\[ X' = (2) + 2(x_3 - 2) = 2 + 2x_3 - 4 = 2x_3 - 2 \] \[ Y' = (0) + 2(y_3 - 0) = 2y_3 \]
So the dilated coordinates will be:
- For point \(X\): \(X' = (2x_1 - 2, 2y_1)\)
- For point \(Y\): \(Y' = (2x_2 - 2, 2y_2)\)
- For point \(Z\): \(Z' = (2x_3 - 2, 2y_3)\)
If you provide the original coordinates of points \(X\), \(Y\), and \(Z\), we can calculate the exact coordinates of \(X'\), \(Y'\), and \(Z'\).
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