Select the coordinates A′

Question

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)
.

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 \( A' \) and \( B' \) after dilation with a scale factor of 13 centered at the origin, we apply the following formula for dilation:

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

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

Given:

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

Now we calculate the dilated coordinates:

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

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

Now we have:

• \( A'(-78, 39) \)
• \( B'(-156, 117) \)

None of the options provided match these calculations, as they appear to be different from what we found. Therefore, based on the process, the correct dilated coordinates should be \( A'(-78, 39) \) and \( B'(-156, 117) \).