Question

Choose the correct answer.

Jake, Edmund, Kim, and Maria were in Washington, D.C., attending a rally. One of the rally events was a walking race that began at a point near the center of Lincoln Park. The red group was to walk west along E. Capitol St. NE for 420 m, then north on 8th St. SE for 200 m, then southeast on Massachusetts Ave. NE back to the starting point in Lincoln Park. The blue team was to walk east on E. Capitol St. NE for 420 m, north on 14th St. SE for 200 m, then southwest on North Carolina Ave. NE back to the starting point.

Street map

Use the Pythagorean Theorem to calculate the distance from the corner of 8th St. SE and Massachusetts Ave. NE to the starting point in Lincoln Park. (Round to one decimal place.)


310.9 m

465.2 m

840 m

620.4 m

Answer 1

Using the Pythagorean Theorem, the distance from the corner of 8th St. SE and Massachusetts Ave. NE to the starting point in Lincoln Park is about 465.2 meters. This is the hypotenuse of a right triangle formed by the walking path, with sides of 420 meters and 200 meters.

Step-by-step explanation:

To calculate the distance from the corner of 8th St. SE and Massachusetts Ave. NE to the starting point in Lincoln Park using the Pythagorean Theorem, we can visualize the red group's walking race path as two sides of a right triangle, and the distance we want to find is the hypotenuse of this triangle.

The two sides are as follows:

• One side along E. Capitol St. NE (the base of this triangle) is 420 m.
• The other side along 8th St. SE (the height of this triangle) is 200 m.

The Pythagorean Theorem states that in a right-angled triangle:

c2 = a2 + b2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Applying this to our situation, we substitute the known values:

c2 = 4202 + 2002

Calculating this gives:

c2 = 176400 + 40000

c2 = 216400

Taking the square root of 216400, we have:

c ≈ 465.2 m

Thus, the correct answer is 465.2 m, which is the distance from the corner of 8th St. SE and Massachusetts Ave. NE to the starting point in Lincoln Park.