Question

Find the distance between the origin and point $A(3,4).$

• A. $4$ units
• B. $6$ units
• C. $5$ units
• D. $3$ units

Answer 1

The correct option is C $5$ units

To find the distance between the origin $(0,0)$ and $(3,4)$:
Plot the points in a coordinate plane. Then, draw a right triangle with a hypotenuse that represents the distance between the points.



Use the Pythagorean theorem to find the length of the hypotenuse.
$a^2+b^2=c^2$ (Write the Pythagorean theorem)
$3^2+4^2=c^2$ (Substitute $3$ for $a$ and $4$ for $b$)
$9+16=c^2$ (Evaluate the powers)
$25=c^2$
$5=c$ (Take the positive square root of each side)
$\Rightarrow$ The distance between the points $(0,0)$ and $(3,4)$ is $5$ units.
$\Rightarrow$ Option B is correct.