Line AB contains point A (1, 2) and point B (-2,-1). Find the coordinates of A' and B' after a dilation with a scale factor of 5 with a center point of dilation at the origin. (1 point)

Question

A' (1, 2) and B (-10, -5)

A (5, 10) and B (10, 5)

A (5, 10) and B (-10, -5)

A (5, 10) and B (-2,-1)

Answer 1

To find the coordinates of points A' and B' after a dilation with a scale factor of 5 from the origin, we use the 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 point.

For point A (1, 2):

\[ A' = (5 \cdot 1, 5 \cdot 2) = (5, 10) \]

For point B (-2, -1):

\[ B' = (5 \cdot -2, 5 \cdot -1) = (-10, -5) \]

Thus, after the dilation, the coordinates are:

A' (5, 10) and B' (-10, -5)

So, the correct option is:

A (5, 10) and B (-10, -5).