What is the gradient of a line that is perpendicular to the line passing through the point… — JAMB UTME

What is the gradient of a line that is perpendicular to the line passing through the points $(2, 5)$ and $(4, 11)$ ?

The gradient of the perpendicular line is

-\frac{1}{3}

The gradient of the line connecting

(2, 5)

and

(4, 11)

m = \frac{11-5}{4-2} = 3

. The gradient of a line perpendicular to it must satisfy

m_1 \cdot m_2 = -1

, yielding

-\frac{1}{3}

Calculate the gradient

m_1

of the line passing through

(2, 5)

and

(4, 11)

m_1 = \frac{11 - 5}{4 - 2} = \frac{6}{2} = 3

The gradient formula between two points

(x_1, y_1)

and

(x_2, y_2)

m = \frac{y_2 - y_1}{x_2 - x_1}

Apply the condition for perpendicular lines to find the required gradient

m_2

m_2 = -\frac{1}{m_1} = -\frac{1}{3}

Two non-vertical lines are perpendicular if and only if the product of their gradients is

-1

(

m_1 \cdot m_2 = -1

Perpendicular Line Gradients

Question