Which point is farther from the origin?

[mathdad]

Which point is farther from the origin?

(3, -2) or (4, 1/2)?

I know the origin is the point (0, 0). This is the location on the xy-plane where the x-axis and y-axis meet. Can the distance formula normally used to calculate how far points on the xy-plane are from each other be applied here? If so, how is the distance formula used in this example?

 

[MarkFL]

What you want to do is calculate the distance of both points from the origin, and then compare these distances...or in fact, you could compare the square of the distances. So, we could write:

$$d_1^2=(3-0)^2+(-2-0)^2=13$$

$$d_2^2=(4-0)^2+\left(\frac{1}{2}-0\right)^2=\frac{65}{4}$$

Since $$\frac{65}{4}>\frac{52}{4}=13$$, we find the second given point is farther from the origin. :D

 

[mathdad]

What you want to do is calculate the distance of both points from the origin, and then compare these distances...or in fact, you could compare the square of the distances. So, we could write:

$$d_1^2=(3-0)^2+(-2-0)^2=13$$

$$d_2^2=(4-0)^2+\left(\frac{1}{2}-0\right)^2=\frac{65}{4}$$

Since $$\frac{65}{4}>\frac{52}{4}=13$$, we find the second given point is farther from the origin. :D

Your way is much faster.