CEMC Cayley

Geometry Difficulty 2.3 Junior Find the answer

Which of the following lines, when drawn together with the $x$ -axis and the $y$ -axis, encloses an isosceles triangle?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since the triangle will include the two axes, then the triangle will have a right angle. For the triangle to be isosceles, the other two angles must be $45^{\circ}$ . For a line to make an angle of $45^{\circ}$ with both axes, it must have slope 1 or -1. Of the given possibilities, the only such line is $y=-x+4$ .

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