Question

1. describe a transformation that takes any point a to any point b. (from unit 1, lesson 17.)

Explanation:

Translation is a transformation that slides every point of a figure or space by the same distance in a given direction. If we have point \(A(x_1,y_1)\) and point \(B(x_2,y_2)\), the translation vector \(\vec{v}=(x_2 - x_1,y_2 - y_1)\) can be used. When we apply the translation \(T(x,y)=(x+(x_2 - x_1),y+(y_2 - y_1))\) to point \(A\), it will be moved to point \(B\).

Answer:

A translation. Specifically, if \(A=(x_1,y_1)\) and \(B=(x_2,y_2)\), the translation \(T(x,y)=(x+(x_2 - x_1),y+(y_2 - y_1))\) takes \(A\) to \(B\).