Question

the figure below has a point marked with a large dot.
first, translate the figure 6 units up.
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, for a point, the \(x -\)coordinate is the horizontal value and \(y -\)coordinate is the vertical value. Looking at the original figure, the marked point has \(x=-6\) and \(y = 3\). So the coordinates of the point in the original figure are \((-6,3)\).

Step2: Translate the point

When we translate a point \((x,y)\) \(k\) units up, the rule is \((x,y + k)\). Here \(k = 6\), \(x=-6\) and \(y = 3\). Using the translation rule \((x,y)\to(x,y + 6)\), we substitute \(x=-6\) and \(y = 3\) into the formula. So \(y+6=3 + 6=9\) and \(x\) remains \(-6\).

Answer:

Point in original figure: \((-6,3)\)
Point in final figure: \((-6,9)\)