Question

if foot of the perpendicular drawn from (1,4)To the line L is (2,5);Then the equation of L is ​

Answer 1

Given: the foot of the perpendicular drawn from (1, 4) to the line L is (2, 5)

To find: the equation of L

Solution:

• The equation of the perpendicular passing through the points (1, 4) and (2, 5) is
• (y - 4)/(4 - 5) = (x - 1)/(1 - 2)
• or, (y - 4)/(- 1) = (x - 1)/(- 1)
• or, y - 4 = x - 1
• or, x - y + 3 = 0

Since this line x - y + 3 = 0 is perpendicular to the line L, let the equation of L be

• x + y + k = 0, where k is constant

Since L passes through the point (2, 5), we have

• 2 + 5 + k = 0
• or, k = - 7

Thus the equation of L is

• x + y - 7 = 0 or, x + y = 7

Answer: equation of L is x + y = 7.