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There is a tree that grows directly between Romeo and Juliet's houses. On a graph of the city, Romeo's house is at (-6,-3) and Juliet's house is at (-4,7). Assuming that they could walk directly toward each other's house, in a straight line, and meet at the tree, at what coordinate point would they meet? O (-5,2) O (5,4) O (-1,5) O (-2,5) Submit Answer

There is a tree that grows directly between Romeo and Juliet's houses. On a graph of the city, Romeo's house is at (-6,-3) and Juliet's house is at (-4,7). Assuming that they could walk directly toward each other's house, in a straight line, and meet at the tree, at what coordinate point would they meet? O (-5,2) O (5,4) O (-1,5) O (-2,5) Submit Answer

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Finding the Meeting Point between Romeo and Juliet's Houses** **Problem Statement:** There is a tree that grows directly between Romeo and Juliet’s houses. On a graph of the city, Romeo’s house is at (-6, -3) and Juliet’s house is at (-4, 7). Assuming that they could walk directly toward each other’s house, in a straight line, and meet at the tree, at what coordinate point would they meet? **Options:** - (5, 4) - (-5, 2) - (-2, 5) - (-1, 5) **Solution Explanation:** To find the coordinate point between Romeo and Juliet’s houses, we need to calculate the midpoint between the two given coordinates. Given coordinates: - Romeo's house: (-6, -3) - Juliet's house: (-4, 7) The formula for finding the midpoint \(M\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \] Applying the values: \[ M = \left(\frac{-6 + (-4)}{2}, \frac{-3 + 7}{2}\right) \] \[ M = \left(\frac{-10}{2}, \frac{4}{2}\right) \] \[ M = (-5, 2) \] Therefore, Romeo and Juliet would meet at the coordinate point \((-5, 2)\). **Correct Answer:** - (-5, 2)
Transcribed Image Text:**Finding the Meeting Point between Romeo and Juliet's Houses** **Problem Statement:** There is a tree that grows directly between Romeo and Juliet’s houses. On a graph of the city, Romeo’s house is at (-6, -3) and Juliet’s house is at (-4, 7). Assuming that they could walk directly toward each other’s house, in a straight line, and meet at the tree, at what coordinate point would they meet? **Options:** - (5, 4) - (-5, 2) - (-2, 5) - (-1, 5) **Solution Explanation:** To find the coordinate point between Romeo and Juliet’s houses, we need to calculate the midpoint between the two given coordinates. Given coordinates: - Romeo's house: (-6, -3) - Juliet's house: (-4, 7) The formula for finding the midpoint \(M\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \] Applying the values: \[ M = \left(\frac{-6 + (-4)}{2}, \frac{-3 + 7}{2}\right) \] \[ M = \left(\frac{-10}{2}, \frac{4}{2}\right) \] \[ M = (-5, 2) \] Therefore, Romeo and Juliet would meet at the coordinate point \((-5, 2)\). **Correct Answer:** - (-5, 2)
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