distance (-1,8),(4,-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:

‖ (4, -2) - (-1, 8) ‖

ⅰ

(4, -2) - (-1, 8)

(4 + 1, - 2 - 8)

‖ (4 + 1, - 2 - 8) ‖

ⓘ Start from

4

and move forward

1

on the number line:

4 + 1

5

■Start from

-2

and move back

8

more on the number line, away from zero:

- 2 - 8

-10

‖ (5, -10) ‖

ⅰ

‖ (5, -10) ‖

\sqrt{5^{2} + {(-10)}^{2}}

\sqrt{5^{2} + {(-10)}^{2}}

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

5^{2}

5 \times 5

25

{(-10)}^{2}

(-10) \times (-10)

100

\sqrt{25 + 100}

ⓘ Parentheses are computed first:

25 + 100

125

\sqrt{125}

ⓘ We look for the largest square dividing

125

25

5^{2}

, and take it out of the root:

\sqrt{125}

\sqrt{25 \times 5}

\sqrt{25} \times \sqrt{5}

5 \times \sqrt{5}

▶Distance:

5 \times \sqrt{5}

The numeric value of:

5 \times \sqrt{5}

is:

5 \times \approx 2.2361

▷

\approx 11.1803