A surveyor measured a building lot. She recorded the crorner points of the lot as M(-80, -210), N(-80, -120), P(130, -120), and Q(130, -120). The coordinates represent the distances, in feet, from the axes of a coordinate grid. Calculate the area of the lot

To calculate the area of the lot, we'll use the coordinates of the four points given: \( M(-80, -210) \), \( N(-80, -120) \), \( P(130, -120) \), and \( Q(130, -210) \).

1. **Identify the Shape**:  
   The coordinates suggest that the lot is a rectangle. We can verify this by checking the side lengths.

2. **Calculate the Side Lengths**:  
   - Length of side \( MN \) (or \( PQ \)):  
     The points \( M \) and \( N \) (as well as \( P \) and \( Q \)) have the same x-coordinates but different y-coordinates.  
     \[
     \text{Length} = |y_2 - y_1| = |-120 - (-210)| = |-120 + 210| = 90 \text{ feet}
     \]
   - Length of side \( NP \) (or \( MQ \)):  
     The points \( N \) and \( P \) (as well as \( M \) and \( Q \)) have the same y-coordinates but different x-coordinates.  
     \[
     \text{Length} = |x_2 - x_1| = |130 - (-80)| = |130 + 80| = 210 \text{ feet}
     \]

3. **Calculate the Area**:  
   The area \( A \) of the rectangle is given by multiplying the lengths of two adjacent sides.
   \[
   A = \text{Length} \times \text{Width} = 90 \times 210 = 18900 \text{ square feet}
   \]

So, the area of the lot is **18,900 square feet**.

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:

1. How would you calculate the area if the lot had been an irregular quadrilateral?
2. How can the distance formula be used to confirm the lengths of the sides?
3. What if the coordinates represented distances in meters instead of feet—how would you convert the area?
4. How would you determine the perimeter of the lot using these coordinates?
5. What is the importance of determining the area and perimeter for a surveyor?

**Tip**: Always check that the figure is indeed a rectangle or square by verifying that opposite sides are equal and all angles are right angles before applying area formulas.

Learn how to calculate the area of a rectangle using given coordinates (-80, -210), (-80, -120), (130, -120), and (130, -210) on a coordinate grid. This problem involves coordinate geometry and area calculation, suitable for students in Grades 6-8.

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