Question: 3. Consider the line segment BC shown here. It is dilated by a scale factor of 2.5.
B = (3, 5)
C = (3, -5)
A line segment in the center/right of the graph is vertical at x = 3, with endpoint B at (3, 5) near the top and endpoint C at (3, -5) near the bottom; point A is at the origin.
A line segment with endpoints B(3, 5) and C(3, -5).
What are the coordinates of B after the dilation?
1. **Problem:** Find the coordinates of point $B$ after a dilation with scale factor $2.5$ centered at the origin.
2. **Rule for dilation from the origin:**
If a point is $(x,y)$ and the scale factor is $k$, then the image is $(kx,ky)$.
3. **Substitute the given point and scale factor:**
$$B'=(2.5\cdot 3,\,2.5\cdot 5)$$
4. **Multiply each coordinate:**
$$B'=(7.5,\,12.5)$$
5. **Answer:** The coordinates of $B$ after the dilation are $\mathbf{(7.5,\,12.5)}$.