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′(6,14)
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

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′(−6,3)
and B′(8,18)

1 answer

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

(x,y)(kx,ky)

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

For point A(3, 7): A=(23,27)=(6,14)

For point B(4, 9): B=(24,29)=(8,18)

Thus, the coordinates after dilation are:

  • A′(6, 14)
  • B′(8, 18)

The correct option is: A′(6,14) and B′(8,18)