Question

Find the distance between the points (-3, 2), (-2,-5)​

Answer 1

EXPLANATION.

Distance between the points,

⇒ A = (-3,2) & B = (-2,-5).

As we know that,

Distance formula : √(x₁ - x₂)² + (y₁ - y₂)².

Using this formula in equation, we get.

⇒ √(-3 - (-2))² + (2 - (-5))².

⇒ √(- 3 + 2)² + (2 + 5)².

⇒ √(-1)² + (7)².

⇒ √1 + 49.

⇒ √50 = 5√2.

                                                                                                                             

MORE INFORMATION.

Area of triangle.

$\sf \implies \Delta = \bigg| \dfrac{1}{2} \bigg| \left[\begin{array}{ccc}x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right] = \dfrac{1}{2} = |x_{1}(y_{2} - y_{3}) \ + x_{2}(y_{3} - y_{1}) \ + x_{3}(y_{1} - y_{2}) |$

(2) = Δ = 1/2[r₁r₂ sin(θ₂ - θ₁) + r₂r₃ sin(θ₃ - θ₂) + r₃r₁ sin(θ₁ - θ₂).

(3) = Area of equilateral triangle = (a²√3/4).

(4) = If area of a triangle is zero, then the points are collinear.

Answer 2

EXPLANATION :-

Distance between the points,

⇒ A = (-3,2) & B = (-2,-5).

As we know that,

Distance formula : √(x₁ - x₂)² + (y₁ - y₂)².

Using this formula in equation, we get.

⇒ √(-3 - (-2))² + (2 - (-5))².

⇒ √(- 3 + 2)² + (2 + 5)².

⇒ √(-1)² + (7)².

⇒ √1 + 49.

⇒ √50 = 5√2.

Answered by - @MissGarmi