select the coordinates A' and B' after the 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)
To find the coordinates A' and B' after the dilation with a scale factor of 2 centered at the origin, we first need to calculate the distance between the origin and points A and B.
For point A(3,7):
Distance from the origin = √(3^2 + 7^2) = √(58) = √58
For point B(4,9):
Distance from the origin = √(4^2 + 9^2) = √(97) = √97
Now, we can find the coordinates of points A' and B' after the dilation by multiplying the distance from the origin to the points by the scale factor (2).
For point A':
Coordinates of A' = (2*3, 2*7) = (6, 14)
For point B':
Coordinates of B' = (2*4, 2*9) = (8, 18)
Therefore, after the dilation with a scale factor of 2 centered at the origin, the coordinates of A' and B' are A' (6,14) and B' (8,18).