Question

find the value of k , if P(4,-2) is the mid point of the line segment joining the points A(5k,3) and B(-k,-7)?
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Answer 1

Step-by-step explanation:

okay so P is mid point of line segment AB

that means the distance of point P from A should be equal to the distance of Point P from B. Therefore from Distance Formula

AP =

$\sqrt{ {(5k - 4)}^{2} + {(3 - ( - 2))}^{2} }$

and

PB=

$\sqrt{ { (- k - 4)}^{2} + {( - 7 + 2)}^{2} }$

equating both the formulas we get a quadratic equation in form of k which on solving gives two values of k

k= 0,2