To find the area of the rectangle formed by the points A, B, C, and D, we first need to determine the coordinates of two pairs of opposite corners (vertices) of the rectangle.
Given the points:
- A (-3, -1)
- B (1, 5)
- C (4, 3)
- D (-3, -3)
We can analyze the coordinates to determine
- the width (horizontal length)
- the height (vertical length) of the rectangle.
Step 1: Identify the edges of the rectangle.
- Vertical edges can be made between points A and D, both having the same x-coordinate (-3).
- Horizontal edges can be made between points A and B, points B and C, etc.
- A direct connection is not possible through B to D or A to C since they do not share the same x or y coordinate.
Step 2: Determine the rectangle's length and width.
The edges are:
-
Vertical edge between A and D:
- The y-coordinates are (-1) and (-3), so the height (h) = |(-1) - (-3)| = |2| = 2 units.
-
Vertical edge between B and C:
- x-coordinate from B (1) to C (4) will be the width (w). The y-coordinates are not needed since we are considering vertical lines here:
- Width (w) = |(4) - (1)| = |3| = 3 units.
Step 3: Calculate the area of the rectangle.
The area (A) of the rectangle can be computed as: \[ A = \text{length} \times \text{width} \] \[ A = \text{height} \times \text{width} = 2 \times 3 = 6 , \text{square units}. \]
Conclusion
Upon using the available coordinates, we find that the rectangle does not align properly and the suggested areas do not match; options provided suggest reconsideration of the rectangle edges or re-verifying how shapes fit into given coordinates.
Since the calculated area does not translate into the options available (11, 22, 26, or 52), we clarify the extent of picking the nearest match or correcting edges for a plausible fit based on constraints.
It is also valid to seek corrections based on overlapping arrangements that might produce valid rectangle shapes.
The area showing may appear inconsistent at first looks unless indicating specific arrangements. Thus double-checking logical edges could yield insights into expected areas leading into the provided choices.
For this rectilinear arrangement using the provided coordinates and vertical/horizontal confirmations, realise:
- Area could be assumed theoretically based on normalized checks, yielding potentially clearer grids leading to thought adjustments for matching area outputs possibly.
- Thus, mismatch notices can signify further options could consider overlaps not visually intrinsic at first analysis.
After thorough efforts, the clearer boundaries confirm all options available aren't fitting abide initial verifications leading practicality checks.
Resultantly, echoing dimension consistency as further attribute checks:
- Stepping down indicates preference to revise in context of computed sketches leading to precise results required herewith.
Re-vectorize rectangle aspect interpretations around alternate listings if persists seek back aligned to reconciliatory area outputs using mixed checks through dimensions along assessments for hopeful resolutions iterations across calculations sought.