Answer:
D. 1 : 2
Step-by-step explanation:
Given:
A(-6, -2),
B(6, 7),
C(-2, 1)
Required:
Ratio of AC : CB
SOLUTION:
Find AC:
[tex] AC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] A(-6, -2) = (x_1, y_1) [/tex]
[tex] C(-2, 1) = (x_2, y_2) [/tex]
[tex] AC = \sqrt{(-2 -(-6))^2 + (1 -(-2))^2} [/tex]
[tex] AC = \sqrt{(4)^2 + (3)^2} [/tex]
[tex] AC = \sqrt{16 + 9} = \sqrt{25} [/tex]
[tex] AC = 5 [/tex]
Find CB:
[tex] CB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] C(-2, 1) = (x_1, y_1) [/tex]
[tex] B(6, 7) = (x_2, y_2) [/tex]
[tex] CB = \sqrt{(6 -(-2))^2 + (7 - 1)^2} [/tex]
[tex] CB = \sqrt{(8)^2 + (6)^2} [/tex]
[tex] CB = \sqrt{64 + 36} = \sqrt{100} [/tex]
[tex] CB = 10 [/tex]
Find AC : CB
AC : CB = 5 : 10 = 1 : 2
