What is the distance between point $G(-4,1)$ and point $H(-12,1)$?
To find the distance between point \(G(-4, 1)\) and point \(H(-12, 1)\), we identify the coordinates of both points. Point \(G\) has an x-coordinate of \(x_G = -4\) and point \(H\) has an x-coordinate of \(x_H = -12\). Both points share the same y-coordinate, \(y = 1\). Because the y-coordinates are identical, the line segment connecting these two points is horizontal, and the distance between them is equal to the absolute difference of their x-coordinates.
The distance \(d\) between two points on the same horizontal line is given by:
\[d = |x_H - x_G|\]
Substituting the known x-coordinates into this formula:
\[d = |-12 - (-4)|\]
\[d = |-12 + 4|\]
\[d = |-8|\]
The absolute value of \(-8\) is \(8\). Therefore, the distance between points \(G\) and \(H\) is \(8\) units.
Understanding how to calculate the distance between two points on a Cartesian plane is a fundamental skill in coordinate geometry. This knowledge can be applied to real-world scenarios, such as measuring the length of a segment on a map where two landmarks share the same latitude, or calculating the distance between two objects placed on the same line in a manufacturing layout. By mastering this concept, you can easily determine distances and dimensions in any two-dimensional grid system.