Hi, Hayesannaliese! There are two ways of solving this.
For right triangles, we can use the Pythagorean theorem. For this, we can see that (-2, 5) is 9 units above (-2, -4) and (6, 5) is 8 units right of (-2, 5). For the Pythagorean theorem, [tex]a^2 + b^2 = c^2[/tex]. Plug in the a and b values below:
[tex](8)^2 + (9)^2 = c^2[/tex]
--> [tex]64 + 81 = c^2[/tex]
---> [tex]145 = c^2[/tex]
----> [tex]\sqrt{145} = c[/tex]
c = 12.04 units
Second method: finding the distance between two points
[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
For this problem, we need to find the distance between (-2, -4) and (6, 5).
So the equation is [tex]\sqrt{(6 - (-2))^2 + (5 - (-4))^2}[/tex]
--> [tex]\sqrt{8^2 + 9^2}[/tex]
---> [tex]\sqrt{64 + 81}[/tex]
----> [tex]\sqrt{145}[/tex]
= 12.04 units.
Hope this was helpful. Good luck. :)
