Question

If the distance between the points (3,p) and (-1,0) is 6 units, then find the value of p

Answer 1

Given :

• Two points :- (3,p) and (-1,0)
• Distance between the two points = 6 units

To find :

• find the value of p

Formula used :

To find distance between two points :- (a,b) and (m,n) , we use distance formula. Given as :-

$\sqrt{ {(m -a )}^{2} + {(n - b)}^{2} }$

Solution :

It is given that two points are :- (3,p) and (-1,0)

According to question :-

$\sqrt{ {( - 1-3 )}^{2} + {(0 - p)}^{2} } = 6$

$\sqrt{ {( - 4)}^{2} + {(p)}^{2} } = 6$

${( - 4)}^{2} + {(p)}^{2} = {6}^{2}$

${(p)}^{2} = {6}^{2} - {( - 4)}^{2}$

${(p)}^{2} = 36 - 16$

${(p)}^{2} = 20$

p = ± √20

ANSWER :

P = ± √20

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You can verify your answer by putting the value of p = ± 20 in (3,p) and by finding out distance between (3,±√20) and (-1,0).

Therefore by applying distance Formula :-

$\sqrt{ {( - 1-3 )}^{2} + {(\pm \sqrt{20} )}^{2} }$

$\sqrt{16 + 20}$

$\sqrt{36} = 6 \: units$

hence verified.

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