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Question

If the distance between the points $$(4, p)$$ and $$(1, 0)$$ is $$5$$, then the value of $$p$$ is:


A
4 only
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B
±4
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C
4 only
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D
0
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Solution

The correct option is B $$\pm 4$$
The given points are $$(1,0)$$ and $$ (4,p)$$  
$$d=\sqrt { { \left( { x }_{ 2 }-{ x }_{ 1 } \right)  }^{ 2 }+{ \left( { y }_{ 2 }-{ y }_{ 1 } \right)  }^{ 2 } }$$
$$\Rightarrow 5 =\sqrt{(4-1)^2+p^2}$$
$$\Rightarrow 25 =(4-1)^2+p^2$$
$$\Rightarrow 25-9=p^2$$
$$\Rightarrow p^2=16$$
$$\Rightarrow p=+4,-4$$

Mathematics

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