JAMB 2014 Mathematics · Question 44

Find the mid point of S(-5, 4) and T(-3, -2)

Options

A.-4, 2
B.4, -2
C.-4, 1
D.4, -1

Answer: C. -4, 1

Explanation written with AI and checked against the answer key

1. Analyze the question

You are asked to find the midpoint of a line segment connecting two points in a Cartesian plane: $S(-5, 4)$ and $T(-3, -2)$ .

2. Explain the concept

To find the midpoint $(x_m, y_m)$ of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ , we use the Midpoint Formula:

x_m = \frac{x_1 + x_2}{2}

y_m = \frac{y_1 + y_2}{2}

Essentially, you are finding the average of the x-coordinates and the average of the y-coordinates.

3. Show the solution

Given the points:

$S(x_1, y_1) = (-5, 4)$
$T(x_2, y_2) = (-3, -2)$

Step 1: Find the x-coordinate of the midpoint ( $x_m$ )

x_m = \frac{-5 + (-3)}{2}

x_m = \frac{-5 - 3}{2}

x_m = \frac{-8}{2} = -4

Step 2: Find the y-coordinate of the midpoint ( $y_m$ )

y_m = \frac{4 + (-2)}{2}

y_m = \frac{4 - 2}{2}

y_m = \frac{2}{2} = 1

The midpoint is $(-4, 1)$ .

4. Identify the answer

Comparing our result $(-4, 1)$ to the given options: A. -4, 2 B. 4, -2 C. -4, 1 D. 4, -1

The correct option is C.

5. Exam Tip

When working with coordinates involving negative numbers, always keep them in brackets (e.g., $+(-2)$ ) to avoid sign errors. A common mistake is to subtract the coordinates instead of adding them; remember that the midpoint formula is an average, so you must always add the values together before dividing by 2.

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