Question

what is the distance from the origin to point p graphed on the complex plane below?
o $sqrt{7}$
o $sqrt{29}$
o 7
o 29

Explanation:

Step1: Identify coordinates of point P

Point P has coordinates (2, - 5) as seen from the graph.

Step2: Apply distance - formula from origin

The distance $d$ from the origin $(0,0)$ to a point $(x,y)$ is $d=\sqrt{(x - 0)^2+(y - 0)^2}=\sqrt{x^{2}+y^{2}}$. Here $x = 2$ and $y=-5$.

Step3: Calculate the distance

$d=\sqrt{2^{2}+(-5)^{2}}=\sqrt{4 + 25}=\sqrt{29}$.

Answer:

$\sqrt{29}$