To find the new coordinates A′ and B′ after dilation of the line segment AB by a scale factor of 2 centered at the origin, we need to double the distance between the origin and the original coordinates of A and B.
The distance from the origin to point A is sqrt((3 - 0)^2 + (7 - 0)^2) = sqrt(9 + 49) = sqrt(58) = approximately 7.62.
The distance from the origin to point B is sqrt((4 - 0)^2 + (9 - 0)^2) = sqrt(16 + 81) = sqrt(97) = approximately 9.85.
After doubling the distances, the new coordinates A′ and B′ can be calculated as follows:
A′ = (2 * 3, 2 * 7) = (6, 14)
B′ = (2 * 4, 2 * 9) = (8, 18)
Therefore, the new coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 2 centered at the origin are A′(6, 14) and B′(8, 18).
Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 2, centered at the origin where the endpoints are A(3,7) and B(4,9) .
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