Gradient of a line 1

The points $A(1,2)$, $B(3,7)$ and $C(5,4)$ form a triangle.

Determine the gradients of the line segments $AB$, $AC$ and $BC$

solution - press button to display

Drawing a diagram is almost always helpful!

triangle

The line segment AB has a gradient given by $$ m_{AB} = \frac{\Delta y}{\Delta x} = \frac{7-2}{3-1} = \frac{5}{2} $$

The line segment AC has a gradient given by $$ m_{AC} = \frac{\Delta y}{\Delta x} = \frac{4-2}{5-1} = \frac{1}{2} $$

The line segment AB has a gradient given by $$ m_{BC} = \frac{\Delta y}{\Delta x} = \frac{4-7}{5-3} = -\frac{3}{2} $$