Question

triangle a is the pre - image in a translation, and triangle b is the image, as shown. how was triangle a translated? six units right four units right four units left six units left

Explanation:

Step1: Analyze the horizontal movement

In a coordinate - plane, translation of a figure horizontally is determined by the change in the \(x\) - coordinate.
Let's assume a point \((x,y)\) in triangle \(A\). After translation, the corresponding point in triangle \(B\) has the same \(y\) - coordinate (since there is no vertical movement as the triangles are at the same vertical level in terms of their shape orientation).
For a horizontal translation, if we consider a vertex of triangle \(A\) (say the left - most vertex of the vertical side). Suppose the \(x\) - coordinate of a vertex of triangle \(A\) is \(x_1\) and the \(x\) - coordinate of the corresponding vertex of triangle \(B\) is \(x_2\).
If we count the number of units between the corresponding \(x\) - coordinates of the vertices of the two triangles.
We can use the formula for horizontal translation \(x\to x + h\), where \(h\) is the horizontal translation.
By counting the number of units between the corresponding points of the two triangles (for example, the left - most point of the vertical side of triangle \(A\) and the left - most point of the vertical side of triangle \(B\)) on the \(x\) - axis.
We observe that if we move from triangle \(A\) to triangle \(B\), we are moving in the negative \(x\) - direction (to the left).
Counting the number of unit squares between the corresponding horizontal positions of the two triangles, we find that the number of units is \(4\).

Answer:

four units left