Answer:
5 units
Step-by-step explanation:
The points are:
[tex]A(-2, 5)[/tex]
[tex]B(-2, -7)[/tex]
[tex]C(-6, -4)[/tex]
Considering the sides as vectors, we have:
[tex]\overrightarrow{AB}, \overrightarrow{AC},\overrightarrow{CB}[/tex]
Once
[tex]\overrightarrow{AC} = C - A =(-6, -4) -(-2, 5) = (-6+2, -4-5) = (-4, -9)[/tex]
[tex]\overrightarrow{AB} = B - A =(-2, -7) -(-2, 5) = (-2+2, -7-5) = (0, -12)[/tex]
[tex]\overrightarrow{CB} = B - C =(-2, -7) -(-6, -4) = (-2+6, -7+4) = (4, -3)[/tex]
[tex]\Vert \overrightarrow{AC} \Vert = \sqrt{x^2 + y^2} = \sqrt{(-4)^2+(-9)^2} = \sqrt{16+81}= \sqrt{97}[/tex]
[tex]\Vert \overrightarrow{AB} \Vert = \sqrt{x^2 + y^2} = \sqrt{0^2+(-12)^2} = \sqrt{144}= 12[/tex]
[tex]\Vert \overrightarrow{CB} \Vert = \sqrt{x^2 + y^2} = \sqrt{4^2+(-3)^2} = \sqrt{16+9}= 5[/tex]
