2761.12 – Collinear Vertices of Squares

If the three vertices $A$ , $B$ , and $C$ in the three adjacent squares shown below are collinear, find the value of $x$ . (The drawing is not to scale.)

Solution

If $A$ , $B$ , and $C$ are co-linear, then the slope of $BC$ equals the slope of $AB$ .

In other words, $\dfrac{3}{4} = \dfrac{y}{7}$ , so that $y = \dfrac{21}{4} = 5.25$ and $x = 7 + y = 7 + 5.25 = 12.25$ .