Question

If the endpoints of AB are at (-4, 5) and (2, -7), what is the length of AB?​

Answer 1

Answer:

The length of AB is $6\sqrt{5}$ units

Step-by-step explanation:

The rule of the distance between two points (x1, y1) and (x2, y2) is

• $d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$

∵ 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

∵ $AB=\sqrt{(2--4)^{2}+(-7-5)^{2} }=\sqrt{(2+4)^{2}+(-12)^{2}}$

∴ $AB=\sqrt{(6)^{2}+144}=\sqrt{36+144}$

∴ $AB=\sqrt{180}=6\sqrt{5}$

∴ The length of AB is $6\sqrt{5}$ units