Question

the figure below has a point marked with a large dot.
first, translate the figure 7 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, the \(x -\)coordinate is the horizontal value and \(y -\)coordinate is the vertical value. For the marked point in the original figure, by looking at the grid, the \(x -\)value is \(5\) and the \(y -\)value is \(- 3\). So the coordinates of the point in the original figure are \((5,-3)\).

Step2: Apply the translation rule

When translating a point \((x,y)\) \(k\) units up, the rule is \((x,y + k)\). Here \(k = 7\). Given the original point \((x,y)=(5,-3)\), after translation, the new \(y -\)coordinate is \(y+7=-3 + 7\).

$$y+7=-3 + 7=4$$

The \(x -\)coordinate remains the same (\(x = 5\)). So the coordinates of the point in the final figure are \((5,4)\).

Answer:

Point in original figure: \((5,-3)\)
Point in final figure: \((5,4)\)