Question

the image point of a after a translation left 1 unit and up 4 units is the point b(-4,0). determine the coordinates of the pre - image point a.

Explanation:

Step1: Understand the translation rules

Translation left \(1\) unit: \(x\) - coordinate \(x'=x - 1\). Translation up \(4\) units: \(y\) - coordinate \(y'=y + 4\). Let the coordinates of point \(A\) be \((x,y)\) and of point \(B\) be \((x',y')=(-4,0)\).

Step2: Reverse the translation for \(x\) - coordinate

We know \(x'=x - 1\). To find \(x\), we use \(x=x'+1\). Substitute \(x'=-4\) into the formula: \(x=-4 + 1=-3\).

Step3: Reverse the translation for \(y\) - coordinate

We know \(y'=y + 4\). To find \(y\), we use \(y=y'-4\). Substitute \(y'=0\) into the formula: \(y=0-4=-4\).

Answer:

$(-3,-4)$