If the points (3, 4) and (X, 1) are equidistant from the origin then the value of x is.

Question

Question

This question was previously asked in

Bihar STET TGT (Maths) Official Paper-I (Held On: 04 Sept, 2023 Shift 2)

Answer 1

Concept -

For two points to be equidistant from the origin, their distances from the origin must be the same.

The distance between any point (x₁, x₂) and the origin $(�_{1}, �_{1})Unknown node type: span$ $(0, 0)$ is given by the distance formula:

$Distance = \sqrt{(�_{1} - 0)^{2} + (�_{1} - 0)^{2}} = \sqrt{�_{1}^{2} + �_{1}^{2}}$

$Explanation -$

Given one point is (3, 4), the distance of this point from the origin is:

$Distance = $\sqrt{(3)^2+(4)^2} =\sqrt{9+16} = \sqrt{25} = 5$$

Now, we need to find the value of $�$ for the point $(�, 1)$ to also have a distance of 5 units from the origin.

Using the distance formula again:

Distance = $√{(x)^2+(1)^2} = 5$

Now squaring both side -

⇒ x² + 1 = 25 ⇒ x2 = 24

⇒ x = ± √ 24 = ± 2√ 6

$Distance = \sqrt{�^{2} + 1^{2}} =Unknown node type: span$ Hence option(2) is correct.