To comply with the Americans with Disabilities Act (ADA), a ramp must have a maximum slope of

Question

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A builder sketched the plans for a ramp into the school. If one end of the ramp is at (0,0) and the other end is at (24,2), does the ramp comply with the ADA?

Responses
A Yes, the slope of the ramp is

, so it complies with the ADA.Yes, the slope of the ramp is 1 over 12 , so it complies with the ADA.
B Yes, the slope of the ramp is

, so it complies with the ADA.Yes, the slope of the ramp is 1 over 24 , so it complies with the ADA.
C No, the slope of the ramp is

, so it does not comply with the ADA.No, the slope of the ramp is 12 over 1 , so it does not comply with the ADA.
D No, the slope of the ramp is

, so it does not comply with the ADA.

Answer 1

To determine whether the ramp complies with the Americans with Disabilities Act (ADA), we need to calculate the slope of the ramp that goes from one end at (0,0) to the other end at (24,2).

The formula for calculating the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

In this case:

• \((x_1, y_1) = (0, 0)\)
• \((x_2, y_2) = (24, 2)\)

Substituting these values into the slope formula:

\[ m = \frac{2 - 0}{24 - 0} = \frac{2}{24} = \frac{1}{12} \]

According to the ADA standards, a ramp must have a maximum slope of 1:12 (which means for every 12 units horizontally, there should be no more than 1 unit vertically).

Since the calculated slope is \( \frac{1}{12} \), the ramp complies with the ADA requirements.

Therefore, the correct response is:

A Yes, the slope of the ramp is 1 over 12 , so it complies with the ADA.