distance (2,4),(6,8) — 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 evaluate:

‖ (6, 8) - (2, 4) ‖

ⅰ

(6, 8) - (2, 4)

(6 - 2, 8 - 4)

‖ (6 - 2, 8 - 4) ‖

ⓘ Start from

6

and move back

2

on the number line:

6 - 2

4

■Start from

8

and move back

4

on the number line:

8 - 4

4

‖ (4, 4) ‖

ⅰ

‖ (4, 4) ‖

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

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

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

4^{2}

4 \times 4

16

\sqrt{16 + 16}

ⓘ Parentheses are computed first:

16 + 16

32

\sqrt{32}

ⓘ We look for the largest square dividing

32

16

4^{2}

, and take it out of the root:

\sqrt{32}

\sqrt{16 \times 2}

\sqrt{16} \times \sqrt{2}

4 \times \sqrt{2}

▶Distance:

4 \times \sqrt{2}

The numeric value of:

4 \times \sqrt{2}

is:

4 \times \approx 1.4142

▷

\approx 5.6569