Question

find the distance of point (3,4) from origin​

Answer 1

Required Answer:-

Question:

• Find the distance between the point (3,4) from origin.

Solution:

Distance between two points is calculated by using the formula given below,

$\rm D = \sqrt{ {(x_{1} - x_{2}) }^{2} + {(y_{2} - y_{1})}^{2} }$

Here,

• x₁ = 3
• x₂ = 0 (Coordinates of origin is (0.0))
• y₁ = 4
• y₂ = 0 (Coordinates of origin is (0.0))

So, distance between these points is,

$\rm = \sqrt{ {(3 - 0)}^{2} + {(4 - 0)}^{2} }$

$\rm = \sqrt{ {3}^{2} + {4}^{2} }$

$\rm = \sqrt{9 + 16}$

$\rm = \sqrt{25}$

$\rm = 5 \ units$

★ Hence, the distance between these points is 5 units.

Alternative Way,

Distance of a point from the origin is calculated by using the formula given,

$\rm D = \sqrt{ {x}^{2} + {y}^{2} }$

Here,

• x = 3
• y = 4

So, distance of the point from the origin will be,

$\rm = \sqrt{ {3}^{2} + {4}^{2} }$

$\rm = \sqrt{9 + 16}$

$\rm = \sqrt{25}$

$\rm = 5 \: units$

★ Hence, the distance between these points is 5 units.

Answer:

• The distance between these points is 5 units.

Answer 2

Question:-

• Find the distance of the point from the origin

Answer:-

Given point: (3, 4)

x2=3

y2=4

At origin(0,0):-

x1=0

y1=0

Now the question is to find the distance of (3, 4) from the origin. But......

•How to calculate the distance of a point from the origin?

=>Distance is calculated using this formula:

Solution:-

Step-by-step explanation:

$\sf \: Distance = \sqrt{(x2 - x1) {}^{2} + (y 2 - y1) {}^{2} } \\ \sf - - - - Solution:- \: - - - - \\ \sf \: Distance = \sqrt{(x2 - x1) {}^{2} + (y 2 - y1) {}^{2} }\\ = \sqrt{(3 - 0) {}^{2} + (4 - 0) {}^{2} } \\ = \sqrt{3 {}^{2} + 4 {}^{2} } \\ = \sqrt{9 + 16} \\ = \sqrt{25} \\ = \sf \: 5 \: units$

Correct Answer:-

• 5 units

•Diagram attached