The document describes solving a real-world problem about meeting a friend at a landmark in Washington D.C. It provides the coordinates of the speaker at the National Gallery of Art and their friend at the Washington Monument. It then calculates the midpoint between the two locations and finds the distances from the midpoint to the Smithsonian Institution and Natural History Museum. It determines that the closest landmark is the Natural History Museum, so that is where they should meet.

1. Determine if the
points (-2,3) (-1,1)
and (2,3) are
vertices of a right
triangle.

2. EXAMPLE 4 Solve a real-world problem
SIGHTSEEING
You and a friend are sightseeing in Washington, D.C.
You are at the National Gallery of Art, and your friend
is at the Washington Monument, as shown on the
map. You want to meet at the landmark that is closest
to the midpoint of your locations. At which landmark
should you meet?

3. EXAMPLE 4 Solve a real-world problem
SOLUTION
Your coordinates are (11, 3), and your friend’s
coordinates are (2, 2). First, find the midpoint of your
locations, which is
x1 + x2 , y1 + y2 11 + 2 , 3+2
( 2 2 )= ( 2 2 ) = (6.5, 2.5).
Next, find the distance from the midpoint to the
Smithsonian Institution, located at (7, 1), and to the
Natural History Museum, located at (7, 3).

4. EXAMPLE 4 Solve a real-world problem
Distance to Smithsonian Institution:
d = (6.5 – 7)2 + (2.5 – 1)2 1.58 units
Distance to Natural History Museum:
d = (6.5 – 7)2 + (2.5 – 3)2 0.71 unit
ANSWER
You should meet at the Natural History Museum.

5. • Worksheet 11.5
• 1-6, 16-21, 22-24, 28
• You may want to put work in your
notebook.