Question

The length of a line segment $12\sqrt{2}$ units. If one end is $(-3,2)$ and the ordinate of the second end is $-10$. Find its abscissa.

Answer 1

One end of the line is $A(-3,2)$

Let the abscissa of the second end $=x$

Then the second end is $B(x,-10)$

Length of the line segment, $AB=12\sqrt{2}$

$\sqrt{(x+3{)}^2+(-10-2{)}^2}=12\sqrt{2}$

$\sqrt{(x+3{)}^2+(-12{)}^2}=12\sqrt{2}$

$\sqrt{(x+3{)}^2+144}=12\sqrt{2}$

Squaring both sides, we get,

$(x+3{)}^2+144=144\times 2$

$(x+3{)}^2=144$

Square root both sides,

$x+3=\pm 12$

$x+3=12$ or $x+3=-12$

$x=9$ or $x=-15$