JAMB 2021 Mathematics · Question 22

P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.

Options

A.6.5 units
B.13.0 units
C.3.5 units
D.7.0 units

Answer: A. 6.5 units

Explanation written with AI and checked against the answer key

Analysis

To find the radius of a circle when the coordinates of the endpoints of its diameter are given, we need to:

Calculate the total length of the diameter using the distance formula.
Divide the diameter by 2, since the radius is half the length of the diameter.

Concept: The Distance Formula

The distance $d$ 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}

Step-by-Step Solution

Step 1: Identify the coordinates

$P(x_1, y_1) = (-6, 1)$
$Q(x_2, y_2) = (6, 6)$

Step 2: Calculate the length of the diameter ( $PQ$ ) Substitute the values into the distance formula:

PQ = \sqrt{(6 - (-6))^2 + (6 - 1)^2}

PQ = \sqrt{(6 + 6)^2 + (5)^2}

PQ = \sqrt{(12)^2 + (5)^2}

PQ = \sqrt{144 + 25}

PQ = \sqrt{169}

PQ = 13 \text{ units}

Step 3: Calculate the radius The radius ( $r$ ) is half of the diameter:

r = \frac{PQ}{2}

r = \frac{13}{2}

r = 6.5 \text{ units}

Conclusion

Comparing our result to the options provided, the correct value is 6.5 units.

Exam Tip

When dealing with coordinate geometry, always be careful with signs when subtracting negative numbers (e.g., $6 - (-6)$ becomes $6 + 6$ ). Also, remember the common Pythagorean triple $(5, 12, 13)$ ; recognizing this can save you time during the exam as you won't need to manually calculate the square root of 169!

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