distance (2,3),(2,5) — 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:

‖ (2, 5) - (2, 3) ‖

ⅰ

(2, 5) - (2, 3)

(2 - 2, 5 - 3)

‖ (2 - 2, 5 - 3) ‖

ⓘ Start from

2

and move back

2

on the number line, down to zero:

2 - 2

0

■Start from

5

and move back

3

on the number line:

5 - 3

2

‖ (0, 2) ‖

ⅰ

‖ (0, 2) ‖

\sqrt{0^{2} + 2^{2}}

\sqrt{0^{2} + 2^{2}}

ⓘ Adding 0 changes nothing:

0 + 2^{2}

2^{2}

■An integer power is a repeated product:

2^{2}

2 \times 2

4

\sqrt{4}

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

\sqrt{4}

2

;

2^{2}

4

▶Distance:

2