distance from (0,0) to (3,4) — step-by-step solution

The distance is the norm of the difference of the points: the square root of the sum of the squared coordinate differences

Let's calculate:

‖ (3, 4) - (0, 0) ‖

ⅰ

(3, 4) - (0, 0)

(3, 4)

‖ (3, 4) ‖

ⅰ

‖ (3, 4) ‖

\sqrt{3^{2} + 4^{2}}

\sqrt{3^{2} + 4^{2}}

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

3^{2}

3 \times 3

9

4^{2}

4 \times 4

16

\sqrt{9 + 16}

ⓘ Parentheses are computed first:

9 + 16

25

\sqrt{25}

ⓘ The square root of a number is the positive number whose square is that number:

\sqrt{25}

5

;

5^{2}

25

▶Distance:

5