GCSE Maths Practice: coordinates

Question 5 of 10

This question explores the relationship between perpendicular lines and their gradients.

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\( \begin{array}{l}\text{If a line has gradient } 3,\ \text{what is the gradient of a perpendicular line?}\end{array} \)

Choose one option:

Multiply the known gradient by the unknown, set equal to -1, solve for the unknown.

Perpendicular lines intersect at right angles. A key property in coordinate geometry is that the product of their gradients is -1. If one line has gradient m1, the other line m2 satisfies m1*m2=-1. For example, if a line has gradient 3, the perpendicular line has gradient m such that 3*m=-1, giving m=-1/3. This property helps find perpendicular slopes, which is essential in constructing shapes, analyzing graphs, and solving real-life problems like determining right angles in structures or navigation. Horizontal lines have gradient 0, vertical lines are undefined, forming special cases. Understanding perpendicular gradients enables checking accuracy when drawing graphs, finding intersection points, and solving geometric problems algebraically. Practicing with different slopes, including fractions and negatives, strengthens comprehension and application of this principle.