Line AB

Question

contains point A (2, −5)
and point B (−3, −2)
. Find the coordinates of A′
and B′
after a dilation with a scale factor of 4 with a center point of dilation at the origin.(1 point)
Responses

A′ (8, 20)
and B′ (12, 8)
upper A prime left parenthesis 8 comma 20 right parenthesis and upper B prime left parenthesis 12 comma 8 right parenthesis

A′ (8, −20)
and B′ (−12, −8)
upper A prime left parenthesis 8 comma negative 20 right parenthesis and upper B prime left parenthesis negative 12 comma negative 8 right parenthesis

A′ (2,−5)
and B′ (−12, −8)
upper A prime left parenthesis 2 comma negative 5 right parenthesis and upper B prime left parenthesis negative 12 comma negative 8 right parenthesis

A′ (8, −20)
and B′ (−3, −2)

Answer 1

To find the coordinates of points \( A' \) and \( B' \) after a dilation from the origin with a scale factor of 4, we can use the formula for dilation, which is given by:

\[ A' = (k \cdot x_A, k \cdot y_A) \] \[ B' = (k \cdot x_B, k \cdot y_B) \]

where \( k \) is the scale factor, \( (x_A, y_A) \) are the coordinates of point \( A \), and \( (x_B, y_B) \) are the coordinates of point \( B \).

Given that:

• Point \( A \) is at \( (2, -5) \)
• Point \( B \) is at \( (-3, -2) \)
• The scale factor \( k = 4 \)

Now, we can calculate the coordinates for \( A' \) and \( B' \):

For point \( A' \): \[ A' = (4 \cdot 2, 4 \cdot -5) = (8, -20) \]

For point \( B' \): \[ B' = (4 \cdot -3, 4 \cdot -2) = (-12, -8) \]

Thus, the coordinates after the dilation are: \[ A' (8, -20) \quad \text{and} \quad B' (-12, -8) \]

The correct response is: A′ (8, −20) and B′ (−12, −8)