Question

Find the value or values of k for which the distance between the points a (k,-5),b(2,7) is 13 units find the value of k for which the distance between the point A K, - 5 and b 2, 7 is 13units
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Answer 1

In this question we will use distance formula:
i.e if we have to find distance b/w (a,b) and (c,d) then the formula used is :
$\sqrt{(a - c) ^{2} + (b - d) ^{2} }$
now distance is already given in the question, so, we only need to put the values and get the answer.

$13 = \sqrt{(k - 2)^{2} \: + (7 - ( - 5)) ^{2} }$
$169 = 144 \: + {(k - 2)}^{2}$
$|k - 2| = 5$
so there are two values of k , i.e there are two points in the plane having distance equivalent to 13 from (2,7).
$k = 7 \: and \: - 3$

Answer 2

HOPE THIS HELPS YOU....