1.2.4Journal:The Distance Formula

Journal

Geometry Sem 2

Points Possible:20

Name:

Jaida Crenshaw

Date:

Scenario:Who Threw the Baseball Farther?

Instructions:

• View the video found on page 1 of this Journal activity.
• Using the information provided in the video, answer the questions below.
• Show your work for all calculations.

The Students' Conjectures:Tre and Hector are trying to figure out who threw the baseball farther in the last game.

1. Complete the table to summarize what you know about each player's throw: (2 points: 1 point for each row of the chart)

PlayerStatementTre

Hector

The baseball field has the following dimensions:

a) The baseball diamond is 90 feet by 90 feet.

b) The pitcher's mound is 60.5 feet from home base.

c) The horizontal distance from the pitcher's mound to the right fielder is 95 feet.

Analyze the Conjecture::

2. Looking at the diagram, who do you think threw the ball farther? (1 point)

Graph the Coordinates:Shift the baseball diamond so that home plate becomes the origin,(0, 0).

3. Find the coordinates for the three bases and graph them below: (3 points: 1 point for each base)

a) Home plate: (0, 0)

b) First base: ( ___ , ___ )

c) Second base: ( ___ , ___ )

d) Third base: ( ___ , ___ )

Tre's Position:

Tre was standing on the pitcher's mound. The pitcher's mound is 60.5 feet from home base.

4. Draw Tre's position at the pitcher's mound as the point (42.78, 42.78) on your diagram above. (1 point)

Calculate Tre's Throw:

5. Using the distance formula, calculate how far Tre threw the ball. (4 points: 2 points for setup, 1 for calculation, 1 for the answer).

Hector's Position:

Hector was standing halfway between first and second base, at the grass line. The grass line is 95 feet from the pitcher's mound.

6. Calculate the coordinates for Hector's position. [Note: We can assume that 95 feet is an approximately horizontal distance from the pitcher's mound to the grass line.] (2 points: 1 forx, 1 fory)

Hector was standing at the coordinate ( ___ , ___ ).

Calculate Hector's Throw:

7. Using the distance formula, calculate how far Hector threw the ball. (4 points: 2 points for setup, 1 for calculation, 1 for the answer).

Making a Decision:

8. Who threw the ball farther, and by how much? (1 point)

Outfield exploration:

Tre and Hector want to calculate the maximum possible throw at this field.

They calculate that the farthest point on the field would be the center fielder standing back at the dead center wall at point (322, 322). Suppose the centerfielder threw the ball from here to home base.

9. How far is this throw? (2 points)

Copyright 2018 Apex Learning Inc. Use of this material is subject to Apex Learning'sTerms of Use. Any unauthorized copying, reuse, or redistribution is prohibited. Apex Learning and the Apex Learning Logo are registered trademarks of Apex Learning Inc.