Exercises: Linear functions as lines in coordinate systems

Two sides of the triangle are coordinate axes. These have a right angle between them, so the triangle is certainly right-angled.The right angle cannot be a base angle in an isosceles triangle, so the legs of equal length are the catheti (axes).

There are two ways to choose a point so that the legs are of equal length:

$Q_1(0|2.5)$ and $Q_2(0|-2.5)$. The triangle is then in the 1st quadrant or in the 4th quadrant. The triangle cannot be in other quadrants since P is on the boundary between the first and fourth.

This gives you a slope triangle for $Q_1$ with slope -1 and one for $Q_2$ with slope 1.

Such a triangle thus occurs for the gradients $m_1=-1$ and $m_2=1$ .