Question

find the equation of line joining the points (3,-1) and (2,3) . also find the equation of the line which is perpendicular to this line and passing through the point (5,2)

Answer 1

Equation of a straight line

Given: the points (3, - 1) and (2, 3)

To find: the equation of the straight line joining the points (3, - 1) and (2, 3)

Solution:

1st one.

• The gradient of the straight line passing through the points (3, - 1) and (2, 3) is
• m = (3 + 1) / (2 - 3) = 4 / (- 1) = - 4
• So the equation of the straight line passing through the points (3, - 1) and (2, 3) is
• y - 3 = - 4 (x - 2)
• or, y - 3 = - 4x + 8
• or, 4x + y = 11

2nd one.

• The straight line perpendicular to the straight line 4x + y = 11 can be written as,
• x - 4y = k, where k is constant
• Given that, the line x - 4y = k passes through the point (5, 2). Then
• 5 - 8 = k or, k = - 3
• Thus the required perpendicular straight line is
• x - 4y = - 3 or, x - 4y + 3 = 0.

Answer:

1. Required line: 4x + y = 11
2. Perpendicular line: x - 4y + 3 = 0