Answer:
The length of AB is [tex]6\sqrt{5}[/tex] units
Step-by-step explanation:
The rule of the distance between two points (x1, y1) and (x2, y2) is
- [tex]d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
∵ The endpoints of AB are (-4, 5) and (2, -7)
→ Let point (-4, 5) be (x1, y1) and point (2, -7) be (x2, y2)
∴ x1 = -4 and y1 = 5
∴ x2 = 2 and y2 = -7
→ Substitute them in the rule above to find the length of AB
∵ [tex]AB=\sqrt{(2--4)^{2}+(-7-5)^{2} }=\sqrt{(2+4)^{2}+(-12)^{2}}[/tex]
∴ [tex]AB=\sqrt{(6)^{2}+144}=\sqrt{36+144}[/tex]
∴ [tex]AB=\sqrt{180}=6\sqrt{5}[/tex]
∴ The length of AB is [tex]6\sqrt{5}[/tex] units
