What are the coordinates of the midpoint of the segment whose endpoints are A(−1, 9) and B(3, 8) ?

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Guest Jan 22, 2018

#1**+2 **

This problem requires knowledge of the midpoint formula. For any two coordinates, \((x_1,y_1)\) and \((x_2,y_2)\), the coordinate of their respective midpoint is located at \(\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\).

Let's plug in those coordinates, shall we?

\(A(-1,9)\text{ and }B(3,8)\) | These are the coordinates given in the original problem. Let's use the formula to find the midpoint. |

\(\left(\frac{-1+3}{2},\frac{9+8}{2}\right)\) | Now, it is a matter of simplifying. |

\(\left(\frac{2}{2},\frac{17}{2}\right)\) | Since the question specifically asks for the coordinates to be written in a decimal format, I will do the conversion, albeit a simple one. |

\((1,8.5)\) | |

If you think about it, the midpoint formula (unlike others) should make sense logically; after all, all you are doing is finding the average of the given coordinates. If this is unclear, maybe this image will help facilitate your understanding of the midpoint formula. When I learned this formula, it definitely helped me.

Source: http://blog.brightstorm.com/wp-content/uploads/2015/04/midpoint31.jpg

TheXSquaredFactor
Jan 22, 2018

#1**+2 **

Best Answer

This problem requires knowledge of the midpoint formula. For any two coordinates, \((x_1,y_1)\) and \((x_2,y_2)\), the coordinate of their respective midpoint is located at \(\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\).

Let's plug in those coordinates, shall we?

\(A(-1,9)\text{ and }B(3,8)\) | These are the coordinates given in the original problem. Let's use the formula to find the midpoint. |

\(\left(\frac{-1+3}{2},\frac{9+8}{2}\right)\) | Now, it is a matter of simplifying. |

\(\left(\frac{2}{2},\frac{17}{2}\right)\) | Since the question specifically asks for the coordinates to be written in a decimal format, I will do the conversion, albeit a simple one. |

\((1,8.5)\) | |

If you think about it, the midpoint formula (unlike others) should make sense logically; after all, all you are doing is finding the average of the given coordinates. If this is unclear, maybe this image will help facilitate your understanding of the midpoint formula. When I learned this formula, it definitely helped me.

Source: http://blog.brightstorm.com/wp-content/uploads/2015/04/midpoint31.jpg

TheXSquaredFactor
Jan 22, 2018