Using the origin as one vertex, plot the vertices of:
A right-angled isosceles triangle.
We can plot a right-angled isosceles triangle using the origin O(0, 0) as the vertex of the right angle. Choose point A(3, 0) on the x-axis and point B(0, 3) on the y-axis. Since the axes are perpendicular, angle AOB is 90°. Also, OA = OB = 3 units. Thus, the vertices are O(0, 0), A(3, 0), and B(0, 3).
An isosceles triangle with one vertex in Quadrant III and the other in Quadrant IV.
We can plot an isosceles triangle using the origin O(0, 0) as one vertex. Choose point A(-2, -3) in Quadrant III and point B(2, -3) in Quadrant IV. The distance OA = ² + (-3)²) = units, and the distance OB = ² + (-3)²) = units. Since OA = OB, the vertices are O(0, 0), A(-2, -3), and B(2, -3), forming an isosceles triangle.
Explanation
For part (i), placing the two equal sides along the x- and y-axes ensures the angle at the origin is 90° (since axes are perpendicular) and the sides are equal, satisfying both right-angled and isosceles conditions. For part (ii), selecting points with opposite x-coordinates and the same y-coordinate in Quadrants III and IV ensures they are mirror images across the y-axis, making their distances from the origin equal, which satisfies the isosceles condition.