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It looks like you are working on a geometry question about finding the distance between two points on a coordinate plane. Based on the image, we have two points on the grid.

We can apply the **distance formula** to find the distance between the two points:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
The two points on the graph are approximately at:
- Point 1: \( (3, 5) \)
- Point 2: \( (7, -5) \)

Now, using the distance formula:

1. \( x_1 = 3 \), \( y_1 = 5 \)
2. \( x_2 = 7 \), \( y_2 = -5 \)

Substitute these into the formula:

\[
d = \sqrt{(7 - 3)^2 + (-5 - 5)^2}
\]
\[
d = \sqrt{(4)^2 + (-10)^2}
\]
\[
d = \sqrt{16 + 100}
\]
\[
d = \sqrt{116}
\]
This simplifies to approximately \( \sqrt{116} \), which is not a perfect square, but its approximate value is around \( 10.77 \).

From the options, the closest answer is **\( \sqrt{97} \)**, so that's the answer to select.

Do you have any questions, or would you like further details?

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Here are 5 related questions you could explore:
1. What is the distance between two points with coordinates \( (2, 3) \) and \( (5, 7) \)?
2. How does the midpoint formula relate to the distance formula?
3. What happens if the points lie on the same vertical or horizontal line?
4. How can the distance formula be derived from the Pythagorean theorem?
5. How do you find the distance in three-dimensional space?

**Tip**: The distance formula is just an application of the Pythagorean theorem, so whenever you're unsure, think of the right triangle formed by the points.

What is the distance between the two points on the coordinate plane shown?

Learn how to calculate the distance between two points on a coordinate plane using the distance formula. In this problem, we find the distance between points (3, 5) and (7, -5), applying the Pythagorean theorem to the right triangle formed by these points.

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