Mastery Check Solutions

Show What You Know

Ayaka, Nancy, and Bryson, were playing a round of mini golf. Each player approached this hole a different way, but all shot a hole-in-one. They decided that the hole winner would be the player whose ball traveled the shortest distance. Determine the hole winner by calculating each player’s shot distance.

Ayaka: From tee #1 banks (deflects) off the right boundary wall at $(5, 0)$

$\begin{matrix} From (- 1, - 6) to (5, 0) & + & From (5, 0) to (- 3, 8) \\ d = \sqrt{{(- 1 - 5)}^{2} + {(- 6 - 0)}^{2}} & + & \sqrt{{(5 - (- 3))}^{2} + {(0 - 8)}^{2}} \\ d = 19.798 \\ d = 19.80 \end{matrix}$

Nancy: From tee #2 banks off the midpoint of the right boundary wall

$\begin{matrix} Midpoint \\ (5, 10) and (5, - 5) \\ (\frac{5 + 5}{2}, \frac{10 + - 5}{2}) \\ (5, 2.5) \\ From (0, - 6) to (5, 2.5) & + & From (5, 2.5) to (- 3, 8) \\ d = \sqrt{{(0 - 5)}^{2} + {(- 6 - 2.5)}^{2}} & + & \sqrt{{(5 - (- 3))}^{2} + {(2.5 - 8)}^{2}} \\ d = 19.569 \\ d = 19.57 \end{matrix}$

Note

Q: What are the two endpoints needed to find the middle of the right boundary wall for this hole?

A: $(5, 10)$ and $(5, - 5)$

Bryson: From tee #3 banks off the right boundary wall at $(5, 7)$

$\begin{matrix} From (1, - 6) to (5, 7) & + & From (5, 7) to (- 3, 8) \\ d = \sqrt{{(1 - 5)}^{2} + {(- 6 - 7)}^{2}} & + & \sqrt{{(5 - (- 3))}^{2} + {(7 - 8)}^{2}} \\ d = 21.663 \\ d = 21.66 \end{matrix}$

Sample: Nancy shot the shortest distance and is the winner of this hole.

Say What You Know

In your own words, talk about what you have learned using the objectives for this lesson and your work on this page.

Note

Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.

Determine the distance between two points on the coordinate plane.
Solve for midpoints and endpoints using the midpoint formula.
Apply distance and midpoint formulas to solve problems.