Triangle ABC with vertices at A(3, 2), B(2, −1), C(−2, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.

Question

A′(−4.5, 2)
A′(3, 3)
A′(4.5, 2)
A′(4.5, 3)

Answer 1

To find the vertex of point A′ after dilating triangle ABC from point A(3, 2) using a scale factor of 1.5, we need to apply the dilation formula. When dilating a point (x, y) by a scale factor \( k \) around the origin (0, 0), the new coordinates (x′, y′) are given by:

\[ x' = k \cdot x \] \[ y' = k \cdot y \]

In this case, \( A(3, 2) \) is being dilated with a scale factor of \( k = 1.5 \).

Let's calculate the new coordinates for point A′:

1. For the x-coordinate: \[ x' = 1.5 \cdot 3 = 4.5 \]

2. For the y-coordinate: \[ y' = 1.5 \cdot 2 = 3 \]

Thus, the new coordinates for point A′ are: \[ A′(4.5, 3) \]

The correct answer is: \[ \text{A′(4.5, 3)} \]