a We are told that Carla and Lance left the campsite and hiked 6 miles directly north, and after that turned and hiked 7 miles east to view a waterfall. Let's use this information to draw a diagram.
As we can see, the distance between the campsite and waterfall is a hypotenuse of the right triangle. We can find it using the Pythagorean Theorem.
a^2+b^2=c^2
Let's substitute a with 6 and b with 7 and solve the equation for c.
We conclude that the waterfall is about 9.2 miles away from the campsite.
b Let's start with graphing our diagram from Part A on a coordinate plane. We will place the campsite at the origin and graph everything else.
We can see that the coordinates of the waterfall are (7,6). It is given that Carla and Lance decided to go directly back to the campsite from the waterfall, but they stopped halfway for lunch. To find the coordinates of that point we will use the Midpoint Formula.
M(x_1+x_2/2,y_1+y_2/2)
Let's substitute the endpoints (0,0) and (7,6) of the segment between the campsite and waterfall into the formula.
