Question

Find the ordinate of point whose abcissa is $4$ and which is at a distance $5$ from $(0,5)$

• A. $1,2$
• B. $2,4$
• C. $2,8$
• D. None

Answer 1

The correct option is C $2,8$

Let the co-ordinates of the points be $(0,5)$ and $(4,y)$

at a distance of $5$ units from each other.

$\therefore$ by distance formula,
$5=\sqrt{(0-4{)}^2+(5-y{)}^2}$

$25=16+y^2-10y+25$
$16+y^2-10y=0$

$y^2-8y-2y+16=0$

$y(y-8)-2(y-8)=0$

$(y-8)(y-2)=0$

$\therefore y=8$ or $y=2$

So, option C is correct.