distance (-2,-8),(-10,-2) — 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:

‖ (-10, -2) - (-2, -8) ‖

ⅰ

(-10, -2) - (-2, -8)

(- 10 + 2, - 2 + 8)

‖ (- 10 + 2, - 2 + 8) ‖

ⓘ Start from

-10

and move forward

2

on the number line, getting closer to zero:

- 10 + 2

-8

■Start from

-2

and move forward

8

on the number line, going past zero:

- 2 + 8

6

‖ (-8, 6) ‖

ⅰ

‖ (-8, 6) ‖

\sqrt{{(-8)}^{2} + 6^{2}}

\sqrt{{(-8)}^{2} + 6^{2}}

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

{(-8)}^{2}

(-8) \times (-8)

64

6^{2}

6 \times 6

36

\sqrt{64 + 36}

ⓘ Parentheses are computed first:

64 + 36

100

\sqrt{100}

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

\sqrt{100}

10

;

10^{2}

100

▶Distance:

10