Question

Which point on x-axis is equidistant from (7,6) and (-3,4)

• A. (2,0)
• B. (3,0)
• C. (-5,0)
• D. (1,0)

Answer 1

The correct option is B (3,0)

Let the required point on the x-axis be $(x,0)$

Given $(x,0)$ is equidistant from $(7,6)$ and $(-3,4)$

$\therefore$Distance between $(x,0)\equiv (x_1,y_1)$ and $(7,6)=(x_2,y_2)$=distance between $(x,0)\equiv (x_1,y_1)$ and $(-3,4)\equiv (x_2,y_2)$

Distance Formula $=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\Rightarrow \sqrt{(7-x{)}^2+(6-0{)}^2}=\sqrt{(-3-x{)}^2+(4-0{)}^2}$

$\Rightarrow 49-14x+x^2+36=9+6x+x^2+16$

$\Rightarrow 85-14x=25+6x$

$\Rightarrow -14x-6x=25-85$

$\Rightarrow -20x=-60$

$\Rightarrow x=3$

$\therefore$ Required point on the $x-axis=(3,0)$