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  • 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

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

Answers (1)

Points are A(4, p) and B(1, 0)

Distance

 \ (AB)\ = 5 (given )\\

Here 

\\{{x}_{1}} =4\ \ {{x}_{2}} =1\\ {{y}_{1}} =p \: \: \: \: \: {{y}_{2}} =0\\

Using distance formula 

\\=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}} \\ AB =\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}} \\ Squaring both sides\\ (1 - 4)\textsuperscript{2} + (0 - p)\textsuperscript{2} = (5)\textsuperscript{2}\\ (-3)\textsuperscript{2} + (p)\textsuperscript{2} = 25\\ 9 + p\textsuperscript{2} = 25\\ p\textsuperscript{2} = 25 - 9\\ p\textsuperscript{2} = 16\\ p = \pm 4\\

Hence, option B is correct.

Posted by

infoexpert21

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