Points and Distance

Collinear Test

Compare exact slopes between consecutive pairs of points to decide whether all three points lie on one line.

Example

Compare slopes to decide whether three plotted points are collinear.

highlighted = computed this step

Step 1 — Plot points

Plot the three test points.

Coordinate plot\text{Coordinate plot}
Collinear test plotPoints A(1, 2), B(3, 6), and C(5, 10).ABC

Step 2 — Slope from A to B

Compute the slope from A to B.

mAB=(6−2)/(3−1)=2m_{AB}=( 6 - 2 )/( 3 - 1 )= \hl{2}

Step 3 — Slope from B to C

Compute the slope from B to C.

mBC=(10−6)/(5−3)=2m_{BC}=( 10 - 6 )/( 5 - 3 )= \hl{2}

Step 4 — Verdict

Compare slopes to decide collinearity.

mAB=mBC⇒collinear: yesm_{AB}=m_{BC}\Rightarrow\text{collinear: yes}
collinear-test Three points are collinear when their slopes match.