To find the coordinates of the vertex $B'$ after the dilation of triangle $ABC$ by a scale factor of 2.5, we need to apply the dilation transformation to the coordinates of point $B(2, -1)$.

The dilation transformation is given by:

$(x', y') = (k \cdot x, k \cdot y)$

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

For point $B$, we have:

• $x = 2$
• $y = -1$
• $k = 2.5$

Applying the dilation:

$x' = 2.5 \cdot 2 = 5$ $y' = 2.5 \cdot (-1) = -2.5$

Thus, the coordinates of point $B'$ are:

$B' = (5, -2.5)$

Would you like more details or have any questions?

Here are 5 related questions:

1. What would the coordinates of point $A'$ be after the dilation?
2. How do you calculate the area of triangle $A'B'C'$ after dilation?
3. If the scale factor was 0.5, what would the new coordinates of $B'$ be?
4. How does a dilation affect the angles of a triangle?
5. What is the effect of a negative scale factor on the coordinates of $B'$?

Tip: In a dilation, all distances from the center of dilation are multiplied by the scale factor, but the angles remain unchanged.