Question

question: the image point of a after a translation right 4 units and up 3 units is the point b(-2,2). determine the coordinates of the pre - image point a. answer: attempt 2 out of 2 (2,5) submit answer show examples

Explanation:

Step1: Recall translation rule

For a translation right \(h\) units and up \(k\) units, the rule is \((x,y)\to(x + h,y + k)\). Here \(h = 4\) and \(k=3\), and the image point is \((x_{2},y_{2})=(-2,2)\). Let the pre - image point be \((x_{1},y_{1})\). Then \(x_{2}=x_{1}+h\) and \(y_{2}=y_{1}+k\).

Step2: Solve for \(x\) - coordinate of pre - image

We know \(x_{2}=x_{1}+h\), so \(x_{1}=x_{2}-h\). Substituting \(x_{2}=-2\) and \(h = 4\), we get \(x_{1}=-2 - 4=-6\).

Step3: Solve for \(y\) - coordinate of pre - image

We know \(y_{2}=y_{1}+k\), so \(y_{1}=y_{2}-k\). Substituting \(y_{2}=2\) and \(k = 3\), we get \(y_{1}=2-3=-1\).

Answer:

\((-6,-1)\)