Question

Given the triangle ABC, with points located at A (-3, 4), B (-2, 4), and C (-3, 2). What is the length of line

segment CB?

Answer 1

The length of line segment CB in triangle ABC, where B is (-2, 4) and C is (-3, 2), is calculated as √5 or approximately 2.236 units using the distance formula.

Step-by-step explanation:

The length of the line segment CB in the triangle ABC, with points A (-3, 4), B (-2, 4), and C (-3, 2), can be found by using the distance formula for two points in the Cartesian coordinate system: \(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\).

For the points B (-2, 4) and C (-3, 2), the calculation is as follows:

1. Identify the coordinates of points B and C: B (-2, 4) and C (-3, 2).
2. Apply the distance formula: \(d_{BC} = \sqrt{(-3-(-2))^2 + (2-4)^2} = \sqrt{(-1)^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5}\).
3. Thus, the length of line segment CB is \(\sqrt{5}\), which is approximately 2.236 units.