Slope in Geometry Math Example 4

Follow the full solution, then compare it with the other examples linked below.

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Points

A(1, 2)

B(4, k)

C(7, 14)

are collinear. Find

k

1
Step 1: For collinear points, the slope from $A$ to $B$ equals the slope from $A$ to $C$ .
2
Step 2: Slope $AC = \dfrac{14-2}{7-1} = \dfrac{12}{6} = 2$ .
3
Step 3: Slope $AB = \dfrac{k-2}{4-1} = \dfrac{k-2}{3}$ . Set equal to $2$ : $\dfrac{k-2}{3} = 2 \Rightarrow k - 2 = 6 \Rightarrow k = 8$ .

Answer

k = 8

Three points are collinear exactly when any two pairs have the same slope. Setting slope

AB

equal to slope

AC

gives a linear equation for the unknown

k

About Slope in Geometry

The steepness of a line expressed as rise over run, connecting the algebraic slope formula to the geometric angle of inclination.

Find the slope of the line through [formula] and [formula]. Describe what the slope tells us about t

A road rises [formula] metres over a horizontal distance of [formula] metres. Express the slope as a

Which of these lines is steeper: [formula] or [formula]? Which has a greater angle with the [formula