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Determine the distance between the points [tex]\((5, -2)\)[/tex] and [tex]\((5, 7)\)[/tex].

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GinnyAnswer
To find the details related to the points [tex]\((5, -2)\)[/tex] and [tex]\((5, 7)\)[/tex]:

1. Identify the coordinates of the points:
- Point 1: [tex]\((5, -2)\)[/tex]
- Point 2: [tex]\((5, 7)\)[/tex]

2. Extract the x and y coordinates from each point:
- For Point 1, [tex]\(x_1 = 5\)[/tex] and [tex]\(y_1 = -2\)[/tex]
- For Point 2, [tex]\(x_2 = 5\)[/tex] and [tex]\(y_2 = 7\)[/tex]

3. Calculate the difference in the y-coordinates:
- The difference in the y-coordinates, referred to as [tex]\(\Delta y\)[/tex], is given by:
[tex]\[ \Delta y = y_2 - y_1 \][/tex]
- Substituting the values:
[tex]\[ \Delta y = 7 - (-2) \][/tex]
[tex]\[ \Delta y = 7 + 2 \][/tex]
- Thus, we have:
[tex]\[ \Delta y = 9 \][/tex]

Hence, the values are:
- [tex]\(y_1 = -2\)[/tex]
- [tex]\(y_2 = 7\)[/tex]
- [tex]\(\Delta y = 9\)[/tex]

These values and steps establish the details of the change in the y-coordinates between the two given points.
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