Question

A map of the town that Annie and Barbara live in can be represented by the Cartesian plane. Annie is located at (3,5) and Barbara says she is located at (-6,2). They agree to meet the midpoint of their current locations. However, it turns out that Barbara read the map wrong, and she is actually at (-10,4). What is the positive difference in the x-coordinates of where they agreed to meet and where they should actually meet?

Answer 1

Difference = 2

Explanation:

Coordinates of location of Annie = (3, 5)

Initial(But Wrong) Coordinates of location of Barbara = (-6, 2)

They agreed to meet at the midpoint of their current location. The formula to calculate the midpoint is:

`((x_(1)+x_(2))/(2) ,(y_(1)+y_(2))/(2))`

Using the values in the above formula, we get:

`((-6+3)/(2),(2+5)/(2))\\\\ =(-1.5,3.5)`

Correct Coordinates of location of Barbara = (-10,4)

So, the correct midpoint between location of Barbara and Annie would be:

`((-10+3)/(2),(4+5)/(2))\\\\ =(-3.5,4.5)`

The x-coordinate of initial mid-point = -1.5

The x-coordinate of actual mid-point = -3.5

The positive difference between the x-coordinates = | -3.5 - (-1.5) |

= | -3.5 + 1.5 |

= | -2 |

= 2

The positive difference in the x-coordinates of where they agreed to meet and where they should actually meet is 2