Write an equation of the line that passes through the given points and is perpendicular to the line. Consider a point ( 2, 3) and the line perpendicular to the required line is y = x + 4.
We will use the concept of straight lines in order to find the equation of the line.
Answer: y = -x + 5 is the required equation of the line which passes through the point (2,3) and is perpendicular to the required line is y = x + 4.
Let us see how we will use the concept of straight lines in order to find the equation of the line.
Explanation:
As we know the product of two perpendicular lines is -1.
Hence, let us consider the slope of our required line as m.
Thus,
m × (slope of line y = x + 4) = -1 --------------- (1)
(Slope of line y = x + 4) = 1 -------------- (2)
Hence, m = -1 [Using (1) and (2)]
Now, let us consider another point (x, y) passing through the required line.
Hence, with the definition of slope considering the points (2,3) and (x, y),
(y - 3) / (x - 2) = -1
⇒ y - 3 = -x + 2
⇒ y = -x + 2 + 3
⇒ y = -x + 5