To find the length of segment AC, we must find the total rise and total run between the two points.
Point C is located at (-5, 5). Point A is located at (3,-1). To find the rise, subtract the y-value of A from the y-value of C:
[tex]5 - (-1) = 6[/tex]
The rise of this segment is 6.
To find the run, subtract the x-value of A from the x-value of C:
[tex]3 - (-5) = 8[/tex]
The run of this segment is 8.
We can use the Pythagorean Theorem to find the length of this segment. The theorem uses the following formula:
[tex]a^{2} + b^{2} = c^{2}[/tex]
The segment represents the hypotenuse, and the rise and run represent the legs of this segment. We know that the two legs' lengths are 6 and 8, so plug them into the equation:
[tex]6^{2} + 8^{2} = c^{2}[/tex]
[tex]36 + 64 = c^{2}[/tex]
[tex]100 = c^{2}[/tex]
Square root both sides to get c by itself:
[tex]\sqrt{100} = 10[/tex]
[tex]c = 10[/tex]
The length of segment AC is 10.
