Question

the figure below has a point marked with a large dot. first, translate the figure 6 units to the left. then, give the coordinates of the marked point in the original figure and the final figure. point in original figure: point in final figure:

Explanation:

Step1: Find the original coordinates

In a coordinate system, the \(x\) - coordinate is the horizontal value and the \(y\) - coordinate is the vertical value. For the point in the original figure, by looking at the graph, the \(x\) - coordinate is \(2\) and the \(y\) - coordinate is \(4\). So the point in the original figure is \((2,4)\).

Step2: Apply the translation rule

The rule for translating a point \((x,y)\) \(a\) units to the left is \((x - a,y)\). Here \(a = 6\), \(x=2\) and \(y = 4\). Substitute \(x\) into \(x - a\): \(x-6=2 - 6=-4\), and \(y\) remains \(4\). So the point in the final figure is \((-4,4)\).

Answer:

Point in original figure: \((2,4)\)
Point in final figure: \((-4,4)\)