Estimable reader: A dialogue appended to problem 42 highlights an unsettling outcome of a widespread approach to mathematics education.


252. Folded triangle


In the diagram is right isosceles triangle ABC, with ∠A = 90°, AB = AC = 4 cm.  Point B is folded over PQ so that it overlaps point D on side AC, and AD = 3 cm.  Determine the length of PQ.

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250. Coordinated triangle

In the diagram is the graph of linear equation y = x + 4 containing two points, P(–3, 1) and Q(4, 8).

Point R(x, 0), located on the x-axis, is such that it can move between points S(–3, 0) and T(4, 0).  Define y as the area of △PRQ.

⒜* Write an equation that expresses y in terms of x.
⒝  Determine the range of values of y.
⒞  Given y = 10, determine the coordinates of point R.