Question

12 what is an expression for the distance between the origin and a point ( p(x,y) )?
a ( d = 0 )
b ( d=sqrt{x^{2}-y^{2}} )
c ( d=sqrt{x^{2}+y^{2}} )
d ( d=sqrt{y^{2}-x^{2}} )

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Identify the points

The origin is \((0,0)\) and the point \(P\) is \((x,y)\). Substitute \(x_1 = 0,y_1 = 0,x_2=x,y_2 = y\) into the distance formula.

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Answer:

C. \(d=\sqrt{x^{2}+y^{2}}\)