Question

Somebody help!!

Answer 1

Given the points (-5,5) and (1,-2):

Let (x1, y1) = (-5,5)
(x2,y2) = (1,-2)

Use the distance formula:

d = √[(x2 — x1)^2 + (y2 — y1)^2]

Plug in the values into the formula:

d = √[(x2 — x1)^2 + (y2 — y1)^2]

d = √[(1 — (-5))^2 + (-2 — 5)^2]

d = √[(1 + 5)^2 + (-7)^2]

d = √[(6)^2 + (-7)^2]

d = √[36 + 49]

d = √[85]
d = 9.2195 or 9.22

Answer 2

See the picture below for a way to construct a right triangle that makes that piece the longest side of the triangle your line segment.

With that setup, you can use they Pythagorean Theorem.

    $7^2 + 6^2 = c^2$

And then solve that for c, keeping in mind c must be positive.

   $\begin{aligned}49 + 36 &= c^2\\85 &= c^2\\\sqrt{85} &= c\end{aligned}$

If you want to use the distance formula, that is just the Pythagorean theorem solved for c:

    $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Applying that to your situation

   $d = \sqrt{(5-(-2))^2+(-5-1)^2} = \sqrt{(7)^2+(-6)^2} = \sqrt{49+36} = \sqrt{85}$