Question

The point on x-axis equidistant from (5, 4) and (–2, 3) is ____ .

• A. (3, 0)
• B. (2, 0)
• C. (4, 0)
• D. (0, 2)

Answer 1

The correct option is B

(2, 0)

We know that y-coordinate of a point on x-axis is always 0.

Therefore, let the point on x-axis equidistant from (5, 4) and (–2, 3) be (x, 0).

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

Distance between (5, 4) and (x, 0) = Distance between (-2, 3) and (x, 0)

$\Rightarrow \sqrt{(x-5{)}^2+(0-4{)}^2}=\sqrt{(x-(-2){)}^2+(0-3{)}^2}$

$\Rightarrow (x-5{)}^2+4^2=(x+2{)}^2+3^2$

$\Rightarrow x^2-10x+41=x^2+4x+13$

$\Rightarrow 14x=28$

$\Rightarrow x=2$

Therefore, the point on x-axis equidistant from (5, 4) and (–2, 3) is (2, 0).