Question

If the distance of a point $A(1,2)$ is 13 units from a point $B(a,14)$, then the value of $a$ is

• A. $a=3$ or $a=-4$
• B. $a=6$ or $a=-4$
• C. $a=-6$ or $a=-4$
• D. $a=4$ or $a=-3$

Answer 1

The correct option is B

$a=6$ or $a=-4$

Given that AB=13 units, where the coordinates of A and B are $(1,2)$ and $(a,14)$ respectively.

Applying distance formula,

$13=\sqrt{(a-1{)}^2+(14-2{)}^2}$

$⟹13=\sqrt{a^2-2a+1+144}$

$⟹13=\sqrt{a^2-2a+145}$

Squaring both the sides,

$169=a^2-2a+145$

$⟹a^2-2a-24=0$

$⟹a^2-6a+4a-24=0$

$⟹a(a-6)+4(a-6)=0$

$⟹(a-6)(a+4)=0$

$⟹a=6$ or $a=-4$