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Question: The distance of P (a, b) from the origin is A. \({a^2} + {b^2}\) B. \(|a - b|\) C. \(|a + b|\)...

The distance of P (a, b) from the origin is
A. a2+b2{a^2} + {b^2}
B. ∣a−b∣|a - b|
C. ∣a+b∣|a + b|
D. a2+b2\sqrt {{a^2} + {b^2}}

Explanation

Solution

The question mention that we have to find the distance of point P which is (a, b) from the origin that is (0,0) here we can use the formula of distance finding is (x2−x1)2+(y2−y1)2\sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} . The formula is used to find the length of a line that stretches between two points that is point P and point of origin.

Complete step-by-step answer:
In the question we have one-point P (a, b) and the second point is origin (0, 0)
For finding the distance in geometry we can use the formula of finding distance between two
= (x2−x1)2+(y2−y1)2\sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}}
Here we have
x1=0{x_1} = 0
x2=a{x_2} = a
y1=0{y_1} = 0
y2=b{y_2} = b
Putting the values in the formula we get
=(a−0)2+(b−0)2= \sqrt {{{(a - 0)}^2} + {{(b - 0)}^2}}
=a2+b2= \sqrt {{a^2} + {b^2}}

So, the correct answer is “Option D”.

Note: Here students get confused between the point as the question mentions only one point and for the second point the question says that the word origin in which student gets confused. Always remember the origin means point (0 ,0). Write the values of the points in the terms x1,x2,y1,y2{x_1}, {x_2}, {y_1}, {y_2}. x1{x_1} is the horizontal coordinate of point 1 and x2{x_2} is the horizontal coordinates of point 2. y1{y_1} is the vertical coordinates of point 1 and the y2{y_2} is the vertical coordinates of point 2. The formula is used to find the length of a line that stretches between two points that is point 1 and point 2.