Question

correct answer will be marked as brainlist​

Answer 1

EXPLANATION.

Area of triangle formed by points,

⇒ (1,6) , (3,1) , (10,y) is 20.5 sq. units.

As we know that,

Formula of area of triangle.

⇒ 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)].

⇒ x₁ = 1 , y₁ = 6.

⇒ x₂ = 3 , y₂ = 1.

⇒ x₃ = 10 , y₃ = y.

Put the value in the equation, we get.

⇒ 1/2[1(1 - y) + 3(y - 6) + 10(6 - 1)] = 10.5

⇒ (1 - y) + 3(y - 6) + 10(5) = 21.

⇒ 1 - y + 3y - 18 + 50 = 21.

⇒ 2y  - 18 + 1 + 50 - 21 = 0.

⇒ 2y - 39 + 51 = 0.

⇒ 2y + 12 = 0.

⇒ 2y = -12.

⇒ y = -6.

                                                                                                                             

MORE INFORMATION.

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

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