Find the equations to the sides of the triangles the coordinates of wh

1.	Find the equations to the sides of the triangles the coordinates of whose angular points are respectively: (0,1), (2, 0) and (-1, - 2)
Answer» Given: Points A (0, 1), B(2, 0) and C(-1, -2). Assuming: m₁, m₂ and m₃ be the slope of the sides AB, BC and CA, respectively. Concept Used: The slope of the line passing through the two points (x₁, y₁) and (x₂, y₂). The equation of the line passing through the two points (x₁, y₁) and (x₂, y₂). To find: The equation of sides of the triangle. Explanation: m₁ = \(\frac{0-1}{2-0}\) , m₂ = \(\frac{-2-0}{-1-2}\) , m₃= \(\frac{1+2}{1+0}\) m₁ =\(-\frac{1}{2}\) , m₂ = \(-\frac{2}{3}\) and m₃ = 3 So, the equation of the sides AB, BC and CA are Formula used: y – y₁= m (x – x₁) y - 1 = \(\frac{1}{2}\)(x - 0), y - 0 = -\(\frac{2}{3}\) (x - 2)and y + 2 = 3(x+1) ⇒ x + 2y = 2, 2x – 3y =4 and 3x – y +1 = 0 Hence, equation of sides are x + 2y = 2, 2x – 3y =4 and 3x – y +1 = 0

Find the equations to the sides of the triangles the coordinates of whose angular points are respectively: (0,1), (2, 0) and (-1, - 2)

Answer»

Given:

Points A (0, 1), B(2, 0) and C(-1, -2).

Assuming:

m₁, m₂ and m₃ be the slope of the sides AB, BC and CA, respectively.

Concept Used:

The slope of the line passing through the two points (x₁, y₁) and (x₂, y₂).

The equation of the line passing through the two points (x₁, y₁) and (x₂, y₂).

To find:

The equation of sides of the triangle.

Explanation:

m₁ = \(\frac{0-1}{2-0}\) , m₂ = \(\frac{-2-0}{-1-2}\) , m₃= \(\frac{1+2}{1+0}\)

m₁ =\(-\frac{1}{2}\) , m₂ = \(-\frac{2}{3}\) and m₃ = 3

So, the equation of the sides AB, BC and CA are

Formula used: y – y₁= m (x – x₁)

y - 1 = \(\frac{1}{2}\)(x - 0), y - 0 = -\(\frac{2}{3}\) (x - 2)and y + 2 = 3(x+1)

⇒ x + 2y = 2, 2x – 3y =4 and 3x – y +1 = 0

Hence, equation of sides are x + 2y = 2, 2x – 3y =4 and 3x – y +1 = 0