There are 4 units between points A and B. There are 6 units between points B and C. Since the three points form a right triangle, we can use the Pythagorean Theorem to find the distance between points A and C. The Pythagorean Theorem is:
[tex]b = \sqrt{ {a}^{2} + {c}^{2} } [/tex]
For this problem, we say the length AC is equal to the square root of AB squared plus BC squared. Since AB is 4 units and BC is 6 units, we can say that
[tex]ac = \sqrt{ {4}^{2} + {6}^{2} } [/tex]
Which is
[tex]ac = \sqrt{16 + 36} [/tex]
Which simplifies to
[tex]ac = \sqrt{52} [/tex]
Therefore, the answer is C) root 52
