Question

the distance between p(2,7) and q(-6,n) is pq=10 to find value of n
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Answer 1

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Given :

The distance between P(2,7) and q(-6,n) is 10

To Find :

The value of n

We use distance formula here

$\bold{\boxed{D= \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }}}$

$D = \sqrt{ {( - 6 - 2)}^{2} + {(n - 7)}^{2} }$

$= \sqrt{ {( - 8)}^{2} + {(n - 7)}^{2} } = 10$

$= \sqrt{64 + {(n - 7)}^{2} } = 10$

$= > 8 + \sqrt{ {(n - 7)}^{2} } = 10$

$= > \sqrt{ {(n - 7)}^{2} } = 10 - 8 = 2$

=>Power of root is 1/2 so,

$=> { {(n - 7)}^{2} }^{ \frac{1}{2} }=2$

$= > n - 7 = 2$

$= > n = 7 + 2 = 9$

$\bold{Therefore,value \:of \:n \:is \:9}$