Example Question - image point calculation
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).
Reflecting a Point over y = -x Line
To find the image of a point after a reflection over the line y = x, you would normally swap the x- and y-coordinates of the point. However, the line given in this question is y = -x, which means we need to swap the coordinates and change their signs. The point given is (-7, 5). After reflecting this point over the line y = -x, the x-coordinate becomes -5 and the y-coordinate becomes 7, because you swap them and change the signs. Hence, the image of point (-7, 5) after a reflection over the line y = -x is (-5, 7).
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