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 our 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.
As we know the product of two perpendicular lines is -1.
Hence, let us consider the slope of our required line as m.
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