Question

PLEASE HELP DUE TODAY IM NOT GOOD AT MATH

Answer 1

`\textsf{The midpoint is}\;\left((a+b)/(2),c\right)`

`\textsf{The distance is}\;\;|b-a|\;\;\sf units.`

Explanation:

To find the midpoint of the segment between two points located at (a, c) and (b, c), simply average the x-coordinates and the y-coordinates of these points:

`\textsf{Midpoint}=\left((a+b)/(2),(c+c)/(2)\right)`

`\textsf{Midpoint}=\left((a+b)/(2),(2c)/(2)\right)`

`\textsf{Midpoint}=\left((a+b)/(2),c\right)`

Since the y-coordinates of points (a, c) and (b, c) are the same, they are located on the same horizontal line, y = c. Therefore, to find the distance between the two points, we only need take the absolute value of the difference of their x-coordinates:

`\textsf{Distance}=|b-a|`

Additional information

We take the absolute value of the difference between the x-coordinates when calculating the distance between two points with the same y-coordinate because it ensures that the distance is always positive. This measures the "length" of the line segment between the two points without considering direction.