Example Question - coordinate multiplication
Here are examples of questions we've helped users solve.
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).
Dilation Transformation of a Point
The question asks for the image of the point (-6, -7) after a dilation by a scale factor of 5 centered at the origin. To compute the image of a point after a dilation centered at the origin, you multiply each coordinate of the point by the scale factor. Here, the scale factor is 5. Multiply each coordinate of the point (-6, -7) by 5: - The x-coordinate: -6 * 5 = -30 - The y-coordinate: -7 * 5 = -35 Therefore, the image of the point (-6, -7) after the dilation is (-30, -35).
Point Dilation by Scale Factor at Origin
To find the image of a point after a dilation by a scale factor centered at the origin, you can multiply each coordinate of the point by the scale factor. The given point is \((-4, -8)\), and the scale factor is \(\frac{1}{4}\). Therefore, the image of this point after dilation will be: \((-4 \times \frac{1}{4}, -8 \times \frac{1}{4}) = (-1, -2)\) So the image of the point \((-4, -8)\) after a dilation by a scale factor of \(\frac{1}{4}\) centered at the origin is \((-1, -2)\).
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