Question

the point on x-axis equidistant from the points P(5,0)andQ(-1,0)is : ​

Answer 1

Answer:

(2,0) is the point which is equidistant from the two points

Answer 2

★ Answer ★

From the question we conclude that the point on x-axis would be (x,0). "The ordinate of a point on the x-axis is 0 because the point's y-coordinate is 0. The x-axis is a line of symmetry for the Cartesian coordinate plane, meaning that the y-coordinate of any point on the x-axis is 0."

So, the question is:

(x,0) point is equidistant from the points P(5,0) and Q(-1,0). Find the cordinates of the point.

According to question, the given point (x,0) is equidistant from the two points. So, let d₁ = d₂.

(Refer the attachment)

$∴ \: By \: using:Distance \: formula \: = \sqrt{(x_{2} - x_{1}) ^ 2 + (y_{2} - y_{1}) ^ 2}$

$⇒ \sqrt{{(x + 1)}^{2} + {(0 - 0)}^{2} } = \sqrt{ {(x - 5)}^{2} + {(0 - 0)}^{2} }$

$⇒ {(x - 5)}^{2} = {(x + 1)}^{2}$

$⇒ {x}^{2} + 25 - 10x = {x}^{2} + 1 + 2x$

$⇒10x + 2x = 25 - 1$

$⇒12x = 24$

$⇒x = 2$

∴ The point on x-axis equidistant from the points P(5,0) and Q(-1,0) is (2,0).

Regards,

CreativeAB