Question

Which of the following options is correct with respect to the distances $a$ and $b?$
$a=$ Distance between the points $(3,4)$ and $(-3,4).$
$b=$ Distance between the points $(3,4)$ and $(3,-4).$

• A. $a>b$
• B. $a<b$
• C. $a=b$
• D. None of the above

Answer 1

The correct option is B $a<b$

As per the distance formula, the shortest distance between any two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by $\sqrt{(y_2-y_1{)}^2+(x_2-x_1{)}^2}.$

Given:
$a=$ Distance between the points $(3,4)$ and $(-3,4)$

So, the distance between the two points, $a$
$=\sqrt{(4-4{)}^2+(-3-3{)}^2}$
$=\sqrt{(0{)}^2+(-6{)}^2}$
$=\sqrt{0+36}$
$=\sqrt{36}$
$=6$ units

Given:
$b=$ Distance between the points $(3,4)$ and $(3,-4)$

So, the distance between the two points, $b$
$=\sqrt{(-4-4{)}^2+(3-3{)}^2}$
$=\sqrt{(-8{)}^2+(0{)}^2}$
$=\sqrt{64+0}$
$=\sqrt{64}$
$=8$ units
Hence, $a<b$.
$\Rightarrow$ Option B is correct.