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What is the image of triangle FDH after a dilation with a scale factor 5 Centered at the origin?
To find the image of triangle FDH after a dilation with a scale factor of 5 centered at the origin, each vertex of the triangle must be multiplied by the scale factor. If the original vertices of triangle FDH are (F(x_1, y_1)), (D(x_2, y_2)), and (H(x_3, y_3)), the new vertices after dilation will be (F'(5x_1, 5y_1)), (D'(5x_2, 5y_2)), and (H'(5x_3, 5y_3)). This transformation enlarges the triangle while keeping its shape and orientation.
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A B C Has coordinates of A(6 7) B(4 2) and C(0 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.?
To find the image of points A, B, and C after a dilation centered at the origin with a scale factor of 2, you multiply each coordinate by 2. The new coordinates are A'(12, 14), B'(8, 4), and C'(0, 14). Thus, the images of the points after dilation are A'(12, 14), B'(8, 4), and C'(0, 14).
A triangle with vertices at A(0 0) B(0 4) and C(6 0) is dilated to yield a triangle with vertices at A and prime(0 0) B and prime(0 10) and C and prime(15 0). The origin is the center of dilation. Wha?
To determine the scale factor of the dilation, we can compare the distances from the origin to the vertices of the original triangle and the dilated triangle. The distance from the origin to point B (0, 4) is 4, and to B' (0, 10) is 10. Therefore, the scale factor is ( \frac{10}{4} = 2.5 ). Similarly, for point C, the original distance is 6, and the dilated distance is 15, confirming the scale factor of 2.5.
What is the image of Q for a dilation with center (0 0) and a scale factor of 0.5?
To find the image of point Q under a dilation centered at (0, 0) with a scale factor of 0.5, you multiply the coordinates of Q by 0.5. If Q has coordinates (x, y), the image of Q after dilation will be at (0.5x, 0.5y). This means that the new point will be half the distance from the origin compared to the original point Q.
What is example of dilation?
An example of dilation can be seen in the enlargement of a shape on a coordinate plane. For instance, if a triangle with vertices at (1, 2), (2, 3), and (3, 1) is dilated by a scale factor of 2 from the origin, the new vertices will be at (2, 4), (4, 6), and (6, 2). This transformation increases the size of the triangle while maintaining its proportions and shape.
What are the coordinates of the image of the point (-412) under a dilation with a scale factor of 4 and the center of dilation at the origin?
If the original point was (-4, 12) then the image is (-16, 48).
Triangle ABC below will be dilated with the origin as the center of dilation and scale factor of 1/2?
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A B C Has coordinates of A(6 7) B(4 2) and C(0 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.?
To find the image of points A, B, and C after a dilation centered at the origin with a scale factor of 2, you multiply each coordinate by 2. The new coordinates are A'(12, 14), B'(8, 4), and C'(0, 14). Thus, the images of the points after dilation are A'(12, 14), B'(8, 4), and C'(0, 14).
A triangle with vertices at A(0 0) B(0 4) and C(6 0) is dilated to yield a triangle with vertices at A and prime(0 0) B and prime(0 10) and C and prime(15 0). The origin is the center of dilation. Wha?
To determine the scale factor of the dilation, we can compare the distances from the origin to the vertices of the original triangle and the dilated triangle. The distance from the origin to point B (0, 4) is 4, and to B' (0, 10) is 10. Therefore, the scale factor is ( \frac{10}{4} = 2.5 ). Similarly, for point C, the original distance is 6, and the dilated distance is 15, confirming the scale factor of 2.5.
What is the image of Q for a dilation with center (0 0) and a scale factor of 0.5?
To find the image of point Q under a dilation centered at (0, 0) with a scale factor of 0.5, you multiply the coordinates of Q by 0.5. If Q has coordinates (x, y), the image of Q after dilation will be at (0.5x, 0.5y). This means that the new point will be half the distance from the origin compared to the original point Q.
What is example of dilation?
An example of dilation can be seen in the enlargement of a shape on a coordinate plane. For instance, if a triangle with vertices at (1, 2), (2, 3), and (3, 1) is dilated by a scale factor of 2 from the origin, the new vertices will be at (2, 4), (4, 6), and (6, 2). This transformation increases the size of the triangle while maintaining its proportions and shape.
What are the coordinates of the image of the point (-412) under a dilation with a scale factor of 4 and the center of dilation at the origin?
If the original point was (-4, 12) then the image is (-16, 48).
How do you find the scale factor of the dilation with the center at the origin?
To find the scale factor of a dilation with the center at the origin, you can compare the coordinates of a point before and after the dilation. If a point ( P(x, y) ) is dilated to ( P'(x', y') ), the scale factor ( k ) can be calculated using the formula ( k = \frac{x'}{x} = \frac{y'}{y} ), assuming ( x ) and ( y ) are not zero. This scale factor indicates how much the original point has been enlarged or reduced.
How do you dilate from the origin?
To dilate a shape from the origin, multiply the coordinates of each vertex of the shape by a dilation factor (k). If k is greater than 1, the shape enlarges; if k is between 0 and 1, the shape shrinks. For example, if you have a point (x, y) and the dilation factor is k, the new coordinates after dilation will be (kx, ky). This transformation maintains the shape’s proportions and orientation.
What is the transformation of C(9 3) when dilated by a scale factor of 3 using the origin as the center of dilation?
It is (27, 9).
if i have a dilation of -3 i multiply by -3 right?
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What is the transformation of B(4 8) when dilated by a scale factor of 2 using the origin as the center of dilation?
To find the transformation of point B(4, 8) when dilated by a scale factor of 2 using the origin as the center of dilation, you multiply each coordinate by the scale factor. Thus, the new coordinates will be B'(4 * 2, 8 * 2), which simplifies to B'(8, 16). Therefore, point B(4, 8) transforms to B'(8, 16) after the dilation.
If you take S P O T and dilated it by a scale factor of 3 centered at the origin what are the coordinates of S P O T?
To dilate the points S, P, O, and T by a scale factor of 3 centered at the origin, you multiply the coordinates of each point by 3. If the original coordinates of S, P, O, and T are (x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄) respectively, the new coordinates after dilation will be (3x₁, 3y₁), (3x₂, 3y₂), (3x₃, 3y₃), and (3x₄, 3y₄).
