elect the coordinates A′

Question

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′(6,14)
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′(−6,3)
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′(−4,3)

Answer 1

To find the coordinates of points A' and B' after dilation with a scale factor of 2 centered at the origin, we apply the dilation formula:

\[ A' = (kx, ky) \quad \text{and} \quad B' = (kx, ky) \]

where \( k \) is the scale factor and \( (x, y) \) are the original coordinates.

For point A(3, 7):

\[ A' = (2 \cdot 3, 2 \cdot 7) = (6, 14) \]

For point B(4, 9):

\[ B' = (2 \cdot 4, 2 \cdot 9) = (8, 18) \]

So the coordinates after dilation are:

\[ A'(6, 14) \quad \text{and} \quad B'(8, 18) \]

The correct response is:

A′(6,14) and B′(8,18).