Question

description/rule
each point of a figure is moved the
same ______________________ and in
the same ______________________.

$(x,y) \longrightarrow (x + a, y + b)$

Explanation:

Step1: Recall the definition of translation

In a translation (a type of transformation in geometry), each point of a figure is moved the same distance and in the same direction. The given rule \((x,y)\to(x + a,y + b)\) also shows that we are adding a constant \(a\) (for horizontal movement) and \(b\) (for vertical movement), which means each point is moved a certain distance (determined by \(a\) and \(b\)) in a specific direction (right/left for \(x\)-component, up/down for \(y\)-component).

Step2: Fill in the blanks

The first blank should be "distance" because we move each point by the same length (distance), and the second blank should be "direction" because the movement is in the same orientation (direction) for all points.

Answer:

First blank: distance
Second blank: direction