Question

The three lines given below form a triangle. Find the coordinates of the vertices of the triangle.

Line 1: -3x + 2y = 1 Line 2: 2x + y = 11 Line 3: x + 4y = 9

Answer 1

• (3, 5), (1, 2) and (5, 1)

Explanation:

Make three systems with pairs of lines and solve them to work out the vertices.

1) Line 1 and line 2

• -3x + 2y = 1
• 2x + y = 11

Double the second equation and subtract equations:

• -3x + 2y - 2(2x + y) = 1 - 2(11)
• -3x - 4x = 1 - 22
• -7x = - 21
• x = 3

Find y:

• 2*3 + y = 11
• 6 + y = 11
• y = 11 - 6
• y = 5

The point is (3, 5)

2) Line 1 and line 3

• -3x + 2y = 1
• x + 4y = 9

Triple the second equation and add up equations:

• -3x + 2y + 3(x + 4y) = 1 + 3(9)
• 2y + 12y = 1 + 27
• 14y = 28
• y = 2

Find x:

• x + 4*2 = 9
• x + 8 = 9
• x = 1

The point is (1, 2)

3) Line 2 and line 3

• 2x + y = 11
• x + 4y = 9

Double the second equation and subtract the equations:

• 2x + y - 2(x + 4y) = 11 - 2(9)
• y - 8y = 11 - 18
• - 7y = - 7
• y = 1

Find x:

• x + 4*1 = 9
• x + 4 = 9
• x = 5

The point is (5, 1)