Question

The distance between the origin and a point (x, 4) is 5 units. The value of x is
+2
+
4
+5​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{The distance between the origin and a point (x, 4) is 5 units}$

$\underline{\textsf{To find:}}$

$\textsf{The value of x}$

$\underline{\textsf{Solution:}}$

$\textsf{We know that,}$

$\textsf{The distance betwenen the points}$$\mathsf{(x_1,y_1)}\;\textsf{and}\;\mathsf{(x_2,y_2)}$

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

$\textsf{The distance between the (0,0) and a point (x,4) is 5 units}$

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

$\mathsf{\sqrt{x^2+16}=5}$

$\textsf{Squaring on bothsides we get}$

$\mathsf{x^2+16=25}$

$\mathsf{x^2=9}$

$\textsf{Taking square root on bothsides we get}$

$\mathsf{x=\pm\,3}$

Answer 2

Given:

The distance between the origin and a point (x, 4) is 5 units.

To find:

The value of x is

Solution:

From given, we have,

The distance between the origin and a point (x, 4) is 5 units.

The coordinates of the origin are (0, 0)

Here, we use the distance formula,

d² = (x₂ - x₁)² + (y₂ - y₁)²

For given, we have,

(x₁ , y₁ ) = (0, 0)

(x₂ , y₂ ) = (x, 4)

d = 5

substitute these values in the distance formula,

5² = (x-0)² + (4-0)²

25 = x² + 4²

25 = x² + 16

x² = 25 - 16 = 9

x = 3

Therefore, the value of x is +3.