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Find the value of \(a\) if the distance between the points \((-9\text{ cm}, a\text{ cm})\) and \((3\text{ cm}, 3\text{ cm})\) is \(13\text{ cm}\).

1. 6 cm
2. 8 cm
3. 10 cm
4. 12 cm

Correct answer: 8 cm

Solution

Using the distance formula, \(\sqrt{(3-(-9))^2+(3-a)^2}=13\). This gives \(144+(3-a)^2=169\), so \((3-a)^2=25\), hence \(a=8\) or \(-2\); only \(8\) is in the options.

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