hannah drew a quadrilateral on graph paper. The slopes of the sides are 1/2, 1/2, 0 and 0. She wants to label her drawing. Which shape name is correct based only on the information? Proof and explanation

Answer 1

Based on the slopes of the sides provided, we can analyze the properties of the quadrilateral that Hannah drew.

1. Slopes of the sides:

   • Two sides have a slope of \( \frac{1}{2} \) and two sides have a slope of \( 0 \).

2. Interpretation of slopes:

   • A slope of \( 0 \) indicates that the side is horizontal.
   • A slope of \( \frac{1}{2} \) indicates that the side rises \( 1 \) unit for every \( 2 \) units run horizontally.

3. Shape characteristics:

   • Since there are two horizontal sides (slope \( 0 \)), this suggests that two sides are parallel.
   • The two sides with a slope of \( \frac{1}{2} \) are also parallel since they have the same slope.

4. Conclusion:

   • Since there are two pairs of parallel sides, the shape is a parallelogram.
   • Because the slopes indicate that one pair of sides is horizontal, and the other pair is at a positive angle (rising), the quadrilateral conforms to specific properties of parallelograms.
   • More specifically, if the pairs of slopes were equal (both pairs have the same length and parallel), you could label the shape more distinctly. However, without further information about the lengths of the sides or angles, we can't definitively conclude if it's a rectangle or a general parallelogram.

Thus, based solely on the information about the slopes of the sides, the correct name for the shape Hannah drew is a parallelogram.

Answer 2

also what is the slope ramp shown?
does the ramp comply with ADA?
Why?

Answer 3

Understanding the Slope of a Ramp

When referring to a ramp, the slope often plays a critical role in determining its accessibility, especially in relation to the Americans with Disabilities Act (ADA) standards.

1. Slope Calculation:
   • The slope of a ramp is defined as the ratio of the rise (vertical height) to the run (horizontal distance).
   • For example, if a ramp rises 1 unit vertically over a horizontal distance of 2 units, the slope is calculated as: \[ \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{1}{2} = 0.5. \] In decimal form, this means the ramp rises 0.5 for every 1 unit of horizontal distance.

ADA Ramp Compliance

According to the ADA standards for ramps, the following guidelines are established:

1. Maximum slope for ramps:
   • For wheelchairs, the maximum permissible slope of a ramp is generally \(1:12\) (which is equivalent to a slope of about \(0.083\)), meaning for every inch of vertical rise, there should be at least 12 inches of ramp run.
   • For less than 6 inches of rise, a \(1:10\) slope (0.1) is acceptable.
   • Steeper slopes may be acceptable in some temporary situations or for specific cases, such as in wheelchair lifts, but they must be clearly marked.

Evaluating the Given Slope

• In the case of the ramp with a slope of \( \frac{1}{2} \):
  • This slope implies that for every 2 units of horizontal distance, the ramp rises 1 unit vertically.
  • This translates to a slope ratio of \(1:2\) or simply 2.

Compliance Conclusion

Does the ramp comply with ADA?

• No, it does not comply.
• The ramp's slope of \(1:2\) (or \(0.5\)) is too steep for wheelchair access. It exceeds the maximum ADA guideline slope of \(1:12\), which is necessary to ensure ease of access for individuals using wheelchairs or with mobility impairments.

Summary

The calculated slope of a ramp at \( \frac{1}{2} \) or \(1:2\) does not meet ADA accessibility requirements, rendering it too steep and potentially unsafe for users with disabilities. It's crucial to adhere to ADA guidelines for constructing ramps to ensure they are accessible and safe for all individuals.