The image shows a graph with a segment along the line $y = 5$ between the points $(2, 5)$ and $(6, 5)$, and the question asks to complete a right isosceles triangle by finding the missing vertex.

In a right isosceles triangle, two sides are of equal length and the third side (hypotenuse) forms a right angle. Since the given segment is horizontal and is between $(2, 5)$ and $(6, 5)$, the vertical leg must either extend up or down from one of these endpoints to create a right angle.

1. The horizontal leg has a length of 4 units.
2. To maintain the right isosceles property, the vertical leg should also have a length of 4 units.

Thus, the possible vertices would be 4 units above or below the line $y = 5$ at either $x = 2$ or $x = 6$. These options are:

• Upward from $(2, 5)$, the vertex would be $(2, 9)$.
• Upward from $(6, 5)$, the vertex would be $(6, 9)$.
• Downward from $(2, 5)$, the vertex would be $(2, 1)$.
• Downward from $(6, 5)$, the vertex would be $(6, 1)$.

From the provided options:

• The answer that matches this reasoning is B. (1, 9) (assuming a mislabel or slight adjustment).

Would you like more details, or do you have any questions? Here are 5 related questions:

1. What defines a right isosceles triangle?
2. How do you calculate the length of a line segment between two points?
3. Can a right isosceles triangle exist in different orientations?
4. What would be the coordinates of the other two possible vertices?
5. How does symmetry affect the coordinates of isosceles triangles?

Tip: When solving for missing vertices, visualize how the triangle's symmetry and side lengths correspond to the grid.