Select 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′(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

A′(−6,3)
and B′(8,18)

Answer 1

To find the coordinates after dilation centered at the origin with a scale factor of 2, we multiply both coordinates of the endpoints A and B by the scale factor.

Given points:

• A(3, 7)
• B(4, 9)

Applying the dilation:

For point A:

• A′ = (2 * 3, 2 * 7) = (6, 14)

For point B:

• B′ = (2 * 4, 2 * 9) = (8, 18)

So the coordinates after dilation are:

• A′(6, 14) and B′(8, 18)

Thus, the correct response is: A′(6, 14) and B′(8, 18).