Question

the image point of a after a translation left 4 units and down 1 unit is the point b(-2, -4). determine the coordinates of the pre-image point a.

Explanation:

Step1: Analyze the translation rule

A translation left \(4\) units means \(x\)-coordinate of pre - image \(x\) satisfies \(x-4\) (for the image \(x\)-coordinate). A translation down \(1\) unit means \(y\)-coordinate of pre - image \(y\) satisfies \(y - 1\) (for the image \(y\)-coordinate). Let the coordinates of point \(A\) be \((x,y)\). The image point \(B\) has coordinates \((x-4,y - 1)\).

Step2: Set up equations

We know that \(x-4=-2\) and \(y - 1=-4\).
For the \(x\)-coordinate:

$$
LATEXBLOCK0
$$

For the \(y\)-coordinate:

$$
LATEXBLOCK1
$$

Answer:

The coordinates of point \(A\) are \((2,-3)\)