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I think they threw the ball an equal distance. 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: ( 90 , 0 ) c) Second base: ( 90 , 90 ) d) Third base: ( 0, 90 )
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). sqr(0-42.78)^2+(90-42.78)^2 =63.72 Tre threw the ball 63.72 feet 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 for x, 1 for y) (95,45)
Hector was standing at the coordinate ( 95 , 45 ). 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). sqrt(90-95)^2+(90-45)^2 =5 root 82 = 45.27 Hector threw the ball about 45.3 feet Making a Decision: 8. Who threw the ball farther, and by how much? (1 point) Tre threw the ball further by about 18 feet 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) 455 feet