Question

the figure below has a point marked with a large dot. first, translate the figure 8 units to the right. 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 original coordinates

In a coordinate system, the \(x\) - coordinate is the horizontal value and the \(y\) - coordinate is the vertical value. For the original point, by looking at the graph, the \(x\) - value is \(0\) and the \(y\) - value is \(3\). So the coordinates of the original point are \((0,3)\).

Step2: Apply translation rule

The translation rule for moving a point \(8\) units to the right is \((x,y)\to(x + 8,y)\). Here \(x = 0\) and \(y=3\). Substitute \(x = 0\) into \(x+8\), we get \(0 + 8=8\), and \(y\) remains \(3\).

Answer:

Point in original figure: \((0,3)\)
Point in final figure: \((8,3)\)