Question

A line is of length $10$ m and one end is $(2,-3)$, the $x$ - co-ordinate of the other is $8$, then its $y$- coordinate is:

• A. $5,-11$
• B. $-5,11$
• C. $3,11$
• D. $2,3$

Answer 1

The correct option is A $5,-11$

Let the $y$-coordinate of the other end be $\alpha$

Therefore,

coordinat of other end $=(8,\alpha )$

Now, distance between $(2,-3)$ and $(8,y)$-

$d=\sqrt{{(8-2)}^2+{(y-(-3))}^2}$

Given that length of line is $10$.

$\therefore \sqrt{{(8-2)}^2+{(y-(-3))}^2}=10$

Squaring both sides we have

$36+(y^2+9+6y)=100$

$36+y^2+18y+9=100$

$\Rightarrow y^2+6y-55=0$

$\Rightarrow y^2+11y-5y-55=0$

$\Rightarrow (y+11)(y-5)=0$

$\Rightarrow y=5,-11$

Hence the $y$-coordinate will be $5,-11$.

Hence the correct answer is $\left(A\right)5,-11$.