Example Question - origin
Here are examples of questions we've helped users solve.
Origin of Leonardo Pisano Bigollo
<p>Leonardo Pisano Bigollo, also known as Fibonacci, is from Pisa, Italy.</p>
Dilation of a Point with Scale Factor and Origin
To find the image of a point after a dilation with a scale factor, you multiply each coordinate of the original point by the scale factor. When the dilation is centered at the origin (0, 0), this operation is straightforward. The original point is (-6, 7), and the scale factor is 5. Therefore, you multiply each coordinate of the point by the scale factor: New x-coordinate: -6 * 5 = -30 New y-coordinate: 7 * 5 = 35 So the image of the point (-6, 7) after dilation by a scale factor of 5, centered at the origin, 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 \((-1, -2)\).
Coordinate Plane 90-Degree Rotation
To perform a 90-degree counterclockwise rotation around the origin on a coordinate plane, you can use the following rule: If the original point is (x, y), the coordinates after a 90-degree counterclockwise rotation will be (-y, x). Now let's apply this rule to the vertices of the figure: - For point R (at approximately -7, -3), after rotation it will become (3, -7). - For point S (at approximately -2, -3), after rotation it will become (3, -2). - For point T (at approximately -2, -8), after rotation it will become (8, -2). - For point Q (at approximately -7, -8), after rotation it will become (8, -7). Please verify the exact coordinates on the graph as they could be slightly different from the estimates I provided based on the image.
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