Example Question - image transformation
Here are examples of questions we've helped users solve.
Dilation of a Point
The question is asking for the image of the point (12, −4) after a dilation by a scale factor of \( \frac{1}{3} \), centered at the origin. To find the image of a point after dilation, you multiply the coordinates of the original point by the scale factor. Here the scale factor is \( \frac{1}{3} \). Thus, the transformed coordinates (x', y') of the original point (x, y) = (12, −4) would be calculated by: x' = x * scale factor y' = y * scale factor Calculating these: x' = 12 * \( \frac{1}{3} \) = 4 y' = −4 * \( \frac{1}{3} \) = −\( \frac{4}{3} \) Therefore, the image of the point (12, −4) after the dilation is (4, −\( \frac{4}{3} \)).
Dilation of a Point
The question is asking for the image of the point (6, -4) after a dilation by a scale factor of 3 centered at the origin. Dilation is a transformation that produces an image that is the same shape as the original but is a different size. When dilating a point from the origin, you multiply each coordinate by the scale factor. The original point is (6, -4), and the scale factor is 3, so you would multiply each coordinate of the point by 3: The x-coordinate: 6 * 3 = 18 The y-coordinate: -4 * 3 = -12 So the image of the point (6, -4) after the dilation is (18, -12).
Reflection Over Line
The image contains a question that reads as follows: "What is the image of (−1, −4) after a reflection over the line y = −x?" To find the image of a point after a reflection over the line y = -x, you need to switch the x and y coordinates of the point, and then change the sign of both. The original point is (-1, -4), so after switching the coordinates, you get (-4, -1). Then change the signs to get the reflection: (4, 1). Thus, the image of the point (-1, -4) after a reflection over the line y = -x is (4, 1).
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