In the adjacent squares shown, the vertices A,B, and C lie in a straight line. The value of x is:?

Question

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I always choose best answers. :D

Answer 1

if we place the corner of the diagram at position (0,0) we find that point A = (0,4)
point B = (4,7)
point C = (11, y)

the slope of line going through A and B is (7-4)/(4-0) = 3/4

the equation of the line is

y-y1 = m ( x-x1) let's use (x1, y1) = (0,4)

y - 4 = 3/4 (x - 0)

y = (3x/4) + 4

when x = 11, y will equal

y = 33/4 + 4 = 49/4

since we are dealing with a square the length equals the width.
Therefore x = 49/4

Answer 2

10 ... if they're in a straight line and you're given values as shown you can take the equation for slope ... m = Δy/Δx ... since we only care about x we can take Δx from the two values given... 4-7 = 3... therefore if it continues in a straight line the next value must be 10.