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Question

If the distance between point $${\rm{P}}\left( {{\rm{2,2}}} \right)$$ and $${\rm{Q}}\left( {{\rm{5,x}}} \right)$$ is $$5$$ then the value of $$x$$ is 


A
2
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B
6
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C
3
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D
1
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Solution

The correct option is A $$6$$
We have,
$$P=(2, 2), Q=(5, x)$$ and $$PQ=5$$

We know that
$$d^2=(x_2-x_1)^2+(y_2-y_1)^2$$

Therefore,
$$PQ^2=(5-2)^2+(x-2)^2$$

$$5^2=(3)^2+(x-2)^2$$

$$25=9+(x-2)^2$$

$$(x-2)^2=16$$

$$x-2=\pm 4$$

$$x=6$$ or $$x=-2$$

Hence, this is the answer.

Mathematics

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