Question

find the component form of the vector that translates ( a(-1, -2) ) to ( a(-2, -1) ). enter in the form ( langle a, b
angle ).

Explanation:

Step1: Recall the formula for the component form of a translation vector.

The component form of a vector that translates a point \( (x_1, y_1) \) to \( (x_2, y_2) \) is \( \langle x_2 - x_1, y_2 - y_1
angle \).

Step2: Identify the coordinates of the original and translated points.

Here, the original point \( A \) is \( (-1, -2) \) and the translated point \( A' \) is \( (-2, -1) \). So, \( x_1 = -1 \), \( y_1 = -2 \), \( x_2 = -2 \), and \( y_2 = -1 \).

Step3: Calculate the components of the vector.

For the \( x \)-component: \( x_2 - x_1 = -2 - (-1) = -2 + 1 = -1 \).
For the \( y \)-component: \( y_2 - y_1 = -1 - (-2) = -1 + 2 = 1 \).

Answer:

\(\langle -1, 1
angle\)