Answer:
Length of AB is [tex]\sqrt{106}[/tex]
Step-by-step explanation:
Let us use the rule of the distance To find the length of AB
∵ A = (9, -3)
∵ B = (0, 2)
∴ x1 = 9 and y1 = -3
∴ x2 = 0 and y2 = 2
∵ AB = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
→ Substitute the values of x1, x2, y1, and y2 in the rule to find AB
∴ AB = [tex]\sqrt{(0-9)^{2}+(2--3)^{2}}[/tex]
∴ AB = [tex]\sqrt{(-9)^{2}+(2+3)^{2}}[/tex]
∴ AB = [tex]\sqrt{81+(5)^{2}}[/tex]
∴ AB = [tex]\sqrt{81+25}[/tex]
∴ AB = [tex]\sqrt{106}[/tex]
→ The square root of 106 is the simplest radical form
∴ Length of AB is [tex]\sqrt{106}[/tex]
