Find the coordinates of the vertices of a triangle, the equations of w

1.	Find the coordinates of the vertices of a triangle, the equations of whose sides are : x + y – 4 = 0, 2x – y + 3 0 and x – 3y + 2 = 0
Answer» Given: x + y − 4 = 0, 2x − y + 3 = 0 and x − 3y + 2 = 0 To find: Point of intersection of pair of lines. Concept Used: Point of intersection of two lines. Explanation: x + y − 4 = 0 … (1) 2x − y + 3 = 0 … (2) x − 3y + 2 = 0 … (3) Solving (1) and (2) using cross - multiplication method: \(\frac{x}{3-4},\frac{y}{-8-3}=\frac{1}{-1-2}\) ⇒ \(x=\frac{1}{3},y=\frac{11}{3}\) Solving (1) and (3) using cross - multiplication method: \(\frac{x}{2-12},\frac{y}{-4-2}=\frac{1}{-3-1}\) ⇒ \(x=\frac{5}{2},y=\frac{3}{2}\) Similarly, solving (2) and (3) using cross - multiplication method: \(\frac{x}{-2+9}=\frac{y}{3-4}=\frac{1}{-6+1}\) ⇒ \(x=\frac{7}{5},y=\frac{1}{5}\) Hence, the coordinates of the vertices of the triangle are \(\Big(\frac{1}{3},\frac{11}{3}\Big)\) ,\(\Big(\frac{5}{2},\frac{3}{2}\Big)\) and \(\Big(-\frac{7}{5},\frac{1}{5}\Big)\)

Find the coordinates of the vertices of a triangle, the equations of whose sides are : x + y – 4 = 0, 2x – y + 3 0 and x – 3y + 2 = 0

Answer»

Given:

x + y − 4 = 0, 2x − y + 3 = 0 and x − 3y + 2 = 0

To find: Point of intersection of pair of lines.

Concept Used:

Point of intersection of two lines.

Explanation:

x + y − 4 = 0 … (1)

2x − y + 3 = 0 … (2)

x − 3y + 2 = 0 … (3)

Solving (1) and (2) using cross - multiplication method:

\(\frac{x}{3-4},\frac{y}{-8-3}=\frac{1}{-1-2}\)

⇒ \(x=\frac{1}{3},y=\frac{11}{3}\)

Solving (1) and (3) using cross - multiplication method:

\(\frac{x}{2-12},\frac{y}{-4-2}=\frac{1}{-3-1}\)

⇒ \(x=\frac{5}{2},y=\frac{3}{2}\)

Similarly, solving (2) and (3) using cross - multiplication method:

\(\frac{x}{-2+9}=\frac{y}{3-4}=\frac{1}{-6+1}\)

⇒ \(x=\frac{7}{5},y=\frac{1}{5}\)

Hence, the coordinates of the vertices of the triangle are

\(\Big(\frac{1}{3},\frac{11}{3}\Big)\) ,\(\Big(\frac{5}{2},\frac{3}{2}\Big)\) and \(\Big(-\frac{7}{5},\frac{1}{5}\Big)\)