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

What is the gradient of a straight line that is perpendicular to the line passing through the points $(1, -2)$ and $(5, 6)$ ?

-\frac{1}{2}

The slope of the given line segment is computed as

\frac{6 - (-2)}{5 - 1} = 2

. The perpendicular gradient is the negative reciprocal of

2

, which gives

-\frac{1}{2}

Calculate the gradient of the line passing through the two points

(1, -2)

and

(5, 6)

Using

m_1 = \frac{y_2 - y_1}{x_2 - x_1}

, we obtain

m_1 = \frac{6 - (-2)}{5 - 1} = \frac{8}{4} = 2

The slope of a straight line through two points is defined as the change in

y

divided by the change in

x

Apply the perpendicularity condition to find the perpendicular slope

m_2

Since

m_1 \cdot m_2 = -1

m_2 = -\frac{1}{m_1} = -\frac{1}{2}

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

-1

Perpendicular Line Gradients

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