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:
\[ (x, y) \rightarrow (kx, ky) \]
where \( (x, y) \) are the original coordinates and \( k \) is the scale factor.
For point A(3, 7): \[ A' = (2 \cdot 3, 2 \cdot 7) = (6, 14) \]
For point B(4, 9): \[ B' = (2 \cdot 4, 2 \cdot 9) = (8, 18) \]
Thus, the coordinates after dilation are:
The correct option is: A′(6,14) and B′(8,18)
