Question

The distance between A (1, 3) and B (x, 7) is 5. The value of x if x > 0 is :

• A. 4
• B. 2
• C. 1
• D. 3

Answer 1

The correct option is A 4

Given points are A = (1,3) and B = (x, 7)
$\because$ The distance between two points $(x_1,y_1)\text{and}(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
$\Rightarrow A{B}^2$ = ${(x-1)}^2$ + ${(7-3)}^2$
Given, distance between A and B is 5 units.
$\Rightarrow 5^2={(x-1)}^2$ + 16
$\Rightarrow 9={(x-1)}^2$
$\Rightarrow x-1=\pm 3$
$\Rightarrow x=4,-2$

Since, x > 0
Therefore, the value of 'x' is 4.