Question

Distance between the points $(2,-3)$ and $(5,a)$ is $5$. Hence the value of $a=$............

• A. $-1$
• B. $6$
• C. $1$
• D. $7$

Answer 1

Answer: (C)

$1$

Let the two points be $A(2,-3)$ and $B(5,a)$
$|A-B|=5$

$⟹|A-B{|}^2=25$
$⟹{(2-5)}^2+{(-3-a)}^2=25$
$⟹9+9+6a+a^2=25$
$⟹a^2+6a-7=0$
$⟹a^2+7a-a-7=0$
$⟹(a+7)(a-1)=0$
$⟹a=-7$ or $a=1$
But distance can't be negative
Hence $a=1$