Question

find the component form of the vector that translates a (-2, 0) to a (3, -4). enter in the form langle a, b
angle.

Explanation:

Step1: Recall translation vector formula

To find the translation vector from point \( A(x_1, y_1) \) to \( A'(x_2, y_2) \), we use the formula \( \langle x_2 - x_1, y_2 - y_1
angle \). Here, \( A(-2, 0) \) and \( A'(3, -4) \), so \( x_1=-2, y_1 = 0, x_2 = 3, y_2=-4 \).

Step2: Calculate the x - component

For the x - component \( a \), we calculate \( a=x_2 - x_1=3-(-2)=3 + 2 = 5 \).

Step3: Calculate the y - component

For the y - component \( b \), we calculate \( b=y_2 - y_1=-4 - 0=-4 \).

Answer:

\(\langle 5, - 4
angle\)