Respuesta :

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Answer:

The slope of AB = 2

Step-by-step explanation:

We have a circle described on the triangle. If one side of the triangle is the diameter of the circle, then the triangle is the right triangle.

Therefore m∠B = 90°.

AB is perpendicular to BC.

Let

k: y = m₁x + b₁ and l: y = m₂x + b₂

l ⊥ k ⇔ m₁m₂ = -1 ⇒ m₂ = - 1/m₁

We have the slope of BC m₁ = - 1/2.

Therefore the slope of AB m₂ = - 1/(- 1/2) = 2

The slope of AB is 2.

What is the equation of a line?

The general equation of a line is y = mx + c

where m is the slope of the line and c is the intercept.

What is slope of line?

Slope of line is defined as the angle of line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

We have a circle described on the triangle.

A triangle is said to be a right triangle if one of its sides corresponds to the circle's diameter.

Therefore m∠B = 90°.

AB is perpendicular to BC.

Let the system of two lines

line 1 as y = m₁x + c₁ and

line 2 y = m₂x +c₂

Here line 1 perpendicular to  line 2

So m₁m₂ = -1 ⇒ m₂ = - 1/m₁

The slope of BC m₁ = - 1/2.

So the slope of AB m₂ = - 1/(- 1/2) = 2

Hence, the slope of AB is 2.

Learn more about Slope of Line here:

brainly.com/question/14511992

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