Question

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

A
4 only
B
±4
C
4 only
D
0

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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