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 xx. (The drawing is not to scale.)

2761_12_9a7679e137.png

Solution

If A, B, and C are co-linear, then the slope of BC = slope of AB. In other words, 3/4=y/7 3/4 = y/7, so that y=21/4=5.25y = 21/4 = 5.25 and

x=7+y=7+5.25=12.25.x = 7 + y = 7 + 5.25 = 12.25.