Drawing polygons in the coordinate plane with labeled vertices.

It looks like you've uploaded an image showing a coordinate plane with a polygon drawn using specific points. Let's solve the problem step by step and explain what's going on.

Task: Drawing Polygons in the Coordinate Plane

The image shows a coordinate grid with four labeled points:

- (9, 6)
- (7, 2)
- (4, 2)
- (2, 6)

These points are connected to form a quadrilateral (a four-sided polygon).

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Step-by-Step Analysis

Let’s examine each point and how they are connected:

1. Point A: (2, 6) — located 2 units right and 6 units up
2. Point B: (4, 2) — 4 units right, 2 units up
3. Point C: (7, 2) — 7 units right, 2 units up
4. Point D: (9, 6) — 9 units right, 6 units up

From the diagram:
- The points are connected in order:
(2,6) → (4,2) → (7,2) → (9,6) → back to (2,6)

This forms a closed shape, specifically a trapezoid.

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Why is it a Trapezoid?

A trapezoid has one pair of parallel sides.

Let’s check the slopes of the sides:

#### Side 1: From (2,6) to (4,2)
Slope = (2 - 6)/(4 - 2) = (-4)/2 = -2

#### Side 2: From (4,2) to (7,2)
Slope = (2 - 2)/(7 - 4) = 0/3 = 0 → horizontal line

#### Side 3: From (7,2) to (9,6)
Slope = (6 - 2)/(9 - 7) = 4/2 = 2

#### Side 4: From (9,6) to (2,6)
Slope = (6 - 6)/(2 - 9) = 0/(-7) = 0 → horizontal line

So:
- Side from (4,2) to (7,2): horizontal
- Side from (9,6) to (2,6): horizontal

✔ These two top and bottom sides are parallel (both have slope 0), so this confirms it's a trapezoid.

Also, notice:
- The top side is from (2,6) to (9,6) — length = 9 - 2 = 7 units
- The bottom side is from (4,2) to (7,2) — length = 7 - 4 = 3 units

So it's a trapezoid with parallel bases of 7 and 3 units, and non-parallel legs.

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Conclusion

The polygon formed by connecting the points:

(2,6), (4,2), (7,2), (9,6)

is a trapezoid.

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✔ Final Answer:

The figure is a trapezoid because it has one pair of parallel sides (the top and bottom sides are both horizontal). The vertices are plotted correctly on the coordinate plane as shown.

If the task was to identify the polygon, then the answer is:

> Trapezoid

Let me know if you need to calculate area, perimeter, or verify symmetry!