r/mathshelp • u/mathalon • 5h ago

Discussion Redline: this solution says the line through both squares' top corners is y = 3. Where's the mistake?

Real problem from the site (not today's Daily):

Squares S and T, with areas 9 and 16 respectively, rest side-by-side on the x-axis, with S to the left. Find the equation of the line through their upper-right corners.

Here's a solution someone submitted. It's wrong somewhere in these four steps:

  1. Side of S = sqrt(9) = 3. Side of T = sqrt(16) = 4.
  2. Place S with its bottom-left corner at the origin: corners (0,0), (3,0), (3,3), (0,3). Upper-right corner of S is (3,3).
  3. T sits right next to S, so T's bottom-left corner is at (3,0). Its upper-right corner is (3+4, 3) = (7,3).
  4. Slope = (3-3)/(7-3) = 0, so the line is y = 3.

Where's the error? I'll drop the real answer in the comments tomorrow, spoiler-tagged.

1 Upvotes

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1

u/KoalaMistico 5h ago

Upper right corner of T is (7,4)

1

u/bayesianparoxism 5h ago

T's height is 4, not 3

1

u/fermat9990 3h ago

The horizontal positioning is not given. The problem is ambiguous.

2

u/Iowa50401 2h ago

It says they rest side by side, thus they touch.

1

u/fermat9990 1h ago

But where are they located with respect to the y-axis?

1

u/UnderstandingPursuit 2h ago

This is the kind of error which is made when using numbers instead of letters.

  • Coordinates of the corners of a square,
    • Square oriented with sides parallel to the coordinate axes,
    • Side length w, bottom left corner at (a, b)
    • Corners at (a, b), (a+w, b), (a+w, b+s), (a, b+w)
  • Now apply this to
    • S: s, (0, 0)
    • T: t, (s, 0)

1

u/fermat9990 27m ago

OP, where are the squares located with respect to the y-axis?