What is the distance between the points (-4, -3) and (-4, 8) on the coordinate plane?
The distance \(d\) between two points \(P_1 = (x_1, y_1)\) and \(P_2 = (x_2, y_2)\) on a Cartesian plane is given by the distance formula:
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
We are given the points \(P_1 = (-4, -3)\) and \(P_2 = (-4, 8)\). Here, \(x_1 = -4\), \(y_1 = -3\), \(x_2 = -4\), and \(y_2 = 8\).
Substitute the coordinates of the two points into the distance formula:
\[d = \sqrt{(-4 - (-4))^2 + (8 - (-3))^2}\]
Simplify the expressions inside the parentheses:
\[d = \sqrt{(-4 + 4)^2 + (8 + 3)^2}\]
\[d = \sqrt{0^2 + 11^2}\]
\[d = \sqrt{0 + 121}\]
\[d = \sqrt{121}\]
\[d = 11\]
Since the x-coordinates are the same, the distance is simply the absolute difference between the y-coordinates:
\[d = |y_2 - y_1| = |8 - (-3)| = |11| = 11\]
The distance is 11 units.
The distance between the points \((-4, -3)\) and \((-4, 8)\) is 11 units. Therefore, the correct option is the second one.
Final Answer: \(\boxed{11}\) units.
Imagine you are reading a map where the vertical axis represents the street number and the horizontal axis represents the avenue number. If you are standing at the intersection of Avenue -4 and Street -3, and you need to walk to the intersection of Avenue -4 and Street 8, you are moving strictly along the same avenue. The distance you need to cover is simply the difference between the street numbers: \(|8 - (-3)| = 11\) blocks. This concept of calculating distances along a single axis is fundamental in navigating grids and measuring intervals.