Question

point a(2, 3) is the image of a(3, -4) under a translation. determine the translation. use non-negative numbers. a translation by units to the right/left and units up/down

Explanation:

Step1: Analyze horizontal translation

To find the horizontal translation, we compare the x - coordinates of \(A(3,-4)\) and \(A'(2,3)\). The formula for horizontal translation is \(x_{new}=x_{old}+\Delta x\), where \(\Delta x\) is the horizontal change. So, \(\Delta x=x_{A'}-x_{A}=2 - 3=- 1\). A negative value for \(\Delta x\) means a translation of 1 unit to the left.

Step2: Analyze vertical translation

To find the vertical translation, we compare the y - coordinates of \(A(3,-4)\) and \(A'(2,3)\). The formula for vertical translation is \(y_{new}=y_{old}+\Delta y\), where \(\Delta y\) is the vertical change. So, \(\Delta y = y_{A'}-y_{A}=3-(-4)=3 + 4 = 7\). A positive value for \(\Delta y\) means a translation of 7 units up.

Answer:

A translation by 1 units to the left and 7 units up