Question

If the distance between A (1, 3) and B (x, 7) is 5 then which of the following can be the value of x?

• A. 4
• B. 2
• C. 1
• D. 3

Answer 1

The correct option is A

4

Given A = (1, 3), B = (x, 7) and AB = 5 units

$\because$ Distance between points $(x_1,y_1)$ and$(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.

$\Rightarrow AB$ = $\sqrt{(x-1{)}^2+(7-3{)}^2}$
$\Rightarrow 5^2$ = $(x-1{)}^2+16$
$\Rightarrow 9=(x-1{)}^2$
$\Rightarrow x-1=\pm 3$
$\Rightarrow x=4\left(or\right)-2$