Question

how was triangle a translated?
triangle a is the pre - image in a translation, and triangle b is the image, as shown.

Explanation:

Step1: Analyze the vertical movement

Looking at the \(y -\)coordinates of corresponding points (e.g., the right - angle vertex of the right - triangle). The \(y -\)coordinate of the right - angle vertex of triangle \(A\) is \(y = 4\), and for triangle \(B\) is \(y=-2\). The change in the \(y -\)direction is \(4-(-2)=6\) units down. But the question asks about horizontal translation.

Step2: Analyze the horizontal movement

Looking at the \(x -\)coordinates of corresponding points (e.g., the right - angle vertex of the right - triangle). Let the \(x -\)coordinate of the right - angle vertex of triangle \(A\) be \(x = 1\), and for triangle \(B\) be \(x=-3\). The formula for horizontal translation is \(\Delta x=x_{B}-x_{A}\). Substitute \(x_{A}=1\) and \(x_{B}=-3\) into the formula: \(\Delta x=-3 - 1=-4\). A negative value for \(\Delta x\) means a translation to the left.

Answer:

four units left