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$Graph the image of /_\TUV after a dilation with a scale factor of 5 , centered at the origin.$

Graph the image of $\triangle T U V$ after a dilation with a scale factor of $5$ , centered at the origin.

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Dilations and parallel lines

Full solution

Q. Graph the image of

\triangle T U V

after a dilation with a scale factor of

5

, centered at the origin.

Identify Coordinates: First, we need to identify the coordinates of the vertices of triangle TUV. Let's assume the original coordinates of T, U, and V are $(x_1, y_1)$ , $(x_2, y_2)$ , and $(x_3, y_3)$ respectively. Since the problem does not provide specific coordinates, we will use these variables to represent them.
Apply Dilation: Next, we apply the dilation with a scale factor of $5$ , centered at the origin. To do this, we multiply the $x$ and $y$ coordinates of each vertex by the scale factor. The new coordinates for each vertex will be $(5x_1, 5y_1)$ , $(5x_2, 5y_2)$ , and $(5x_3, 5y_3)$ .
Plot New Coordinates: Now, we plot the new coordinates on a graph. We draw points at $(5x_1, 5y_1)$ , $(5x_2, 5y_2)$ , and $(5x_3, 5y_3)$ . These points represent the vertices of the dilated triangle $T'U'V'$ .
Connect Points: After plotting the points, we connect them with straight lines to form the dilated triangle $T'U'V'$ . This triangle will be $5$ times larger than the original triangle $TUV$ , and its shape will be similar to the original triangle.

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