What is the distance between points (10, 7) and (2, 7) on a coordinate plane?
The problem asks for the distance between two points, \(P_1(10, 7)\) and \(P_2(2, 7)\), on a 2D coordinate plane. We observe that both points share the same y-coordinate, \(y = 7\). This implies that the line segment connecting them is horizontal.
The general distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
Since \(y_1 = y_2 = 7\), the vertical component of the distance \((y_2 - y_1)^2\) becomes \(0^2 = 0\). The formula simplifies to:
\[d = \sqrt{(x_2 - x_1)^2} = |x_2 - x_1|\]
Substituting the x-coordinates \(x_1 = 10\) and \(x_2 = 2\):
\[d = |2 - 10| = |-8| = 8\]
Thus, the distance between the two points is \(8\) units.
Imagine you are tracking the position of a drone moving horizontally across a straight path. If the drone starts at coordinate \(x=2\) and travels to \(x=10\) along the same height line (\(y=7\)), you can calculate the total distance traveled using this formula. This simple method is foundational for navigation, physics, and any field where distance along a grid needs to be quantified.