Question

What is the ratio AC: CB?​

Answer 1

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:

$AC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$A(-6, -2) = (x_1, y_1)$

$C(-2, 1) = (x_2, y_2)$

$AC = \sqrt{(-2 -(-6))^2 + (1 -(-2))^2}$

$AC = \sqrt{(4)^2 + (3)^2}$

$AC = \sqrt{16 + 9} = \sqrt{25}$

$AC = 5$

Find CB:

$CB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$C(-2, 1) = (x_1, y_1)$

$B(6, 7) = (x_2, y_2)$

$CB = \sqrt{(6 -(-2))^2 + (7 - 1)^2}$

$CB = \sqrt{(8)^2 + (6)^2}$

$CB = \sqrt{64 + 36} = \sqrt{100}$

$CB = 10$

Find AC : CB

AC : CB = 5 : 10 = 1 : 2