Question

Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 13 , centered at the origin where the endpoints are A(−6,3) and B(−12,9) .(1 point) Responses A′(−2,1) and B′(−12,9) upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 12 comma 9 right parenthesis A′(−2,1) and B′(−4,3) upper A prime left parenthesis negative 2 comma 1 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis A′(−6,3) and B′(−4,3) upper A prime left parenthesis negative 6 comma 3 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis A′(−18,9) and B′(−36,27)

Answer 1

To find the coordinates of A′ and B′ after dilation with a scale factor of 13, we can use the formula for dilation centered at the origin, which is given by:

\[ (x', y') = (k \cdot x, k \cdot y) \]

where \( k \) is the scale factor.

Given:

• A(−6, 3)
• B(−12, 9)
• Scale factor \( k = 13 \)

Now, let's calculate the new coordinates:

For point A(−6, 3): \[ A′ = (13 \cdot (-6), 13 \cdot 3) = (-78, 39) \]

For point B(−12, 9): \[ B′ = (13 \cdot (-12), 13 \cdot 9) = (-156, 117) \]

So after the dilation, the coordinates are:

• A′(−78, 39)
• B′(−156, 117)

Now comparing with the provided responses, none of the given options match the calculated points. Please verify the problem or the options provided, as there might be a misunderstanding or error in the choices.