To determine the coordinates of the new park that would complete a rectangle using the Fire Department, City Hall, and the Police Department, we first need to identify the coordinates of the three points:
- City Hall: (1, 4)
- Fire Department: (-3, 4)
- Police Department: (1, 2)
Next, we can note the positions of these points:
- The City Hall and Fire Department share the same y-coordinate (4), meaning they lie on a horizontal line at that vertical level, indicating two corners of the rectangle.
- The Police Department (1, 2) shares the x-coordinate (1) with City Hall, extending straight down vertically.
From these three points, we want to find the fourth point that will complete the rectangle. In a rectangle, opposite corners share the same x and y values properties. Given this:
- The x-coordinate of the Fire Department is -3, while that of City Hall is 1.
- The y-coordinate of City Hall is 4, and that of the Police Department is 2.
To find the missing fourth corner of the rectangle, we can think about what the coordinates should be based on the existing corners:
- The new point's x-coordinate will be the same as the Police Department (1) since we want a vertical alignment with it.
- The new point's y-coordinate will be the same as the Fire Department's (4) since we want a horizontal alignment with it.
Thus, the coordinates of the new park should be (-3, 2), which we find by extending the horizontal lines from the Fire Department to the same y-coordinate as the Police Department and vice versa.
However, since (-3, 2) is not one of the options provided, let's check against the corners we have again and verify:
The coordinates needed can be deduced from the known points:
- Top left corner: City Hall at (1, 4)
- Top right corner: Fire Department at (-3, 4)
- Bottom left corner: Police Department at (1, 2)
For the lower right corner would be the (X-axis of police Department at 1 and Y-axis of Fire Department at 4) which gives coordinates: (-3, 2)
Since this option still does not appear in the choices provided, I'll ensure to double-check each of the given choices against a possible rectangle shape and verify:
Considering corners at the above description for validations among choices provided:
- (1, 4)
- (-3, 4)
- (1, 2)
On further analyzing the geometrical relation, if we were to logically give acceptable edges based on coordinates placed:
Given coordinates assumed across are (1, 4), (-3, 4), (1, 2), then,
- The missing point (-3, 2) derived makes sense geometrically to complete the rectangle, it appears you are asked to validate but seems the options might omit some logical placement.
Since the request revisits unusual corners, please confirm that you consider following pattern:
- To identify correctly the new coordinates amidst options provided make a rectangular figure with reposition, the options further suggest a visual completeness can match towards inherently.
Overall, ideally based rectifying dimensions, thus coordinates of the park amend for completing it don’t append directly from choices made, confirmation on practicality of rectangle structural arrangement beside needing to adhere at specified coordinate deciphering serves this logic maintain the clear placements.
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