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Geometry Difficulty 2.3 Junior Find the answer

Which of the following lines, when drawn together with the xx-axis and the yy-axis, encloses an isosceles triangle?

A number or a short expression. Spacing and $ signs are ignored.

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 4545^{\circ}. For a line to make an angle of 4545^{\circ} with both axes, it must have slope 1 or -1. Of the given possibilities, the only such line is y=x+4y=-x+4.

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