Example Question - point dilation
Here are examples of questions we've helped users solve.
Dilation of a Point
To find the image of the point (-8, -4) after a dilation by a scale factor of \( \frac{1}{4} \) centered at the origin, you multiply each coordinate of the original point by the scale factor. So, the new coordinates would be: \( x' = x \cdot \frac{1}{4} = -8 \cdot \frac{1}{4} = -2 \) \( y' = y \cdot \frac{1}{4} = -4 \cdot \frac{1}{4} = -1 \) Therefore, the image of the point (-8, -4) after the dilation is (-2, -1).
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 \((-1, -2)\).
Point Dilation by Scale Factor of 3
The question is asking for the image of the point (0, 6) after a dilation (a type of transformation that resizes objects) by a scale factor of 3, centered at the origin (0, 0). To perform the dilation, you multiply each coordinate of the original point by the scale factor. Since the point is (0, 6) and the scale factor is 3: - Multiply the x-coordinate by 3: 0 * 3 = 0 - Multiply the y-coordinate by 3: 6 * 3 = 18 So the image of the point (0, 6) after the dilation is (0, 18).
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