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) .(1 point) Responses A′(−6,3) and B′(8,18) upper A prime left parenthesis negative 6 comma 3 right parenthesis and upper B prime left parenthesis 8 comma 18 right parenthesis A′(6,14) and B′(−4,3) upper A prime left parenthesis 6 comma 14 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis A′(32,72) and B′(2,92) upper A prime left parenthesis Start Fraction 3 over 2 End Fraction comma Start Fraction 7 over 2 End Fraction right parenthesis and upper B prime left parenthesis 2 comma Start Fraction 9 over 2 End Fraction right parenthesis A′(6,14) and B′(8,18)
To find the coordinates A' and B' after a dilation with a scale factor of 2, centered at the origin, we multiply the x and y coordinates of points A and B by the scale factor.
For point A(3,7):
x-coordinate of A' = 3 * 2 = 6
y-coordinate of A' = 7 * 2 = 14
Therefore, A' = (6,14)
For point B(4,9):
x-coordinate of B' = 4 * 2 = 8
y-coordinate of B' = 9 * 2 = 18
Therefore, B' = (8,18)
The correct answer is A' = (6,14) and B' = (8,18).