Question

A line is of length $10cm$ 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 $5,-11$

length of line of distance between

points $=10cm$

Let one end point be P$(2,-3)$ and

another end point be $(8,y)$

Using distance formula, we get

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

$10=\sqrt{(6{)}^2+(-3-y{)}^2}$

$=\sqrt{36+9+y^2+6y}$

$=\sqrt{45+y^2+6y}$

$100=45+y^2+6y$

$y^2+6y=55$

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

$y^2+11y-5y-55=0$ $\therefore$ Option a is correct

$y=5,-11$