Find the values of y for which the distance between

Find the values of y for which the distance between the points P (2, −3) and Q(10,y) is 10 units.


The distance $d$ between two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by the formula


The distance between two points P(2,3) and Q(10,y) is given as 10 units. Substituting these values in the formula for distance between two points we have,


Now, squaring the above equation on both sides of the equals sign


$100=64+9+y^{2}+6 y$

$27=y^{2}+6 y$

Thus we arrive at a quadratic equation. Let us solve this now,

$y^{2}+6 y-27=0$

$y^{2}+9 y-3 y-27=0$




The roots of the above quadratic equation are thus 3 and −9.

Thus the value of ‘y’ could either be.


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