Triangle ABC with vertices at A(3, 2), B(2, −1), C(−2, 1) is dilated using a scale factor of 2.5 to create triangle A′B′C′. Determine the vertex of point B′.

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.

Learn how to find the coordinates of vertex B' after dilating triangle ABC with vertices at A(3, 2), B(2, -1), C(-2, 1) using a scale factor of 2.5. Understand the dilation transformation formula and its application. Suitable for high school students studying geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation