A line segment is of length 10 units.
Question:

A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is

(a) 9, 6

(b) 3, −9

(c) −3, 9

(d) 9, −6

Solution:

It is given that distance between $\mathrm{P}(2,-3)$ and $\mathrm{Q}(10, y)$ is 10 .

In general, the distance between $\mathrm{A}\left(x_{1}, y_{1}\right)$ and $\mathrm{B}\left(x_{2}, y_{2}\right)$ is given by,

$\mathrm{AB}^{2}=\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}$

So,

$10^{2}=(10-2)^{2}+(y+3)^{2}$

On further simplification,

$(y+3)^{2}=36$

$y=-3 \pm 6$

$=-9,3$

We will neglect the negative value. So,

$y=-9,3$

So the answer is (b)

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