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′(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)
upper A prime left parenthesis 6 comma 14 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
To find the coordinates of A' and B' after dilation with a scale factor of 2, centered at the origin, you need to multiply the x and y-coordinates of A and B by the scale factor.
For point A(3, 7):
- Multiply the x-coordinate, 3, by the scale factor 2 to get 3 * 2 = 6.
- Multiply the y-coordinate, 7, by the scale factor 2 to get 7 * 2 = 14.
Therefore, A' has coordinates (6, 14).
For point B(4, 9):
- Multiply the x-coordinate, 4, by the scale factor 2 to get 4 * 2 = 8.
- Multiply the y-coordinate, 9, by the scale factor 2 to get 9 * 2 = 18.
Therefore, B' has coordinates (8, 18).
Hence, the correct answer is A′(6,14) and B′(8,18).