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
B
6
C
3
D
1

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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