Question

the vector that translates a(-2, 7) to a(6, 4) is < , >.

Explanation:

Step1: Find the horizontal change

To find the horizontal component of the translation vector, subtract the x - coordinate of the original point from the x - coordinate of the translated point. Let the original point be \(A(-2,7)\) and the translated point be \(A'(6,4)\). The horizontal change \(h\) is given by \(h=x_{A'}-x_{A}\).
Substituting the values, we get \(h = 6-(-2)=6 + 2=8\).

Step2: Find the vertical change

To find the vertical component of the translation vector, subtract the y - coordinate of the original point from the y - coordinate of the translated point. The vertical change \(v\) is given by \(v=y_{A'}-y_{A}\).
Substituting the values, we get \(v=4 - 7=-3\).

Answer:

\(\langle8, - 3
angle\)