Find the distance between the points (-2,-3) and (-2,4)

1. Analyze the question

We are asked to find the distance between two points on a Cartesian plane: $P_1(-2, -3)$ and $P_2(-2, 4)$.

2. Explain the concept

The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the distance formula:

Observation: Notice that the $x$-coordinates for both points are the same ($x_1 = -2$ and $x_2 = -2$). When the $x$-coordinates are identical, the line connecting the points is a vertical line. In this case, the distance is simply the absolute difference between the $y$-coordinates:

3. Show the solution

Using the coordinates $P_1(-2, -3)$ and $P_2(-2, 4)$:

• $x_1 = -2, y_1 = -3$
• $x_2 = -2, y_2 = 4$

Method 1 (Using the formula):

Method 2 (Vertical distance shortcut): Since the $x$-coordinates are the same, the distance is the vertical change:

4. Identify the answer

Comparing our result to the given options, the distance is 7.0 units. Note that while the options include "m" (meters), the calculation yields a scalar value of 7.

The correct option is D.

5. Exam Tip

Whenever you see two points with the same $x$-coordinate, don't waste time with the full square root formula! Just subtract the $y$-values. If the $y$-coordinates were the same, you would just subtract the $x$-values. This saves precious time during your JAMB exam.