Practice Geometric Constraints in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Conditions that limit or restrict the possible positions, sizes, or shapes of geometric objects in a problem.
A door hinge constrains the door to swing in an arc, not slide sideways.
Example 1
easyA point P is constrained to lie on a circle of radius 5 centred at the origin AND on the line y = x + 1. Find all possible positions of P.
Example 2
mediumA rectangle has perimeter 36 cm and one side of length x. Write the constraint for the other side, and determine the range of valid values for x.
Example 3
easyA point P(x, y) must satisfy: (1) it is in the first quadrant, and (2) its distance from the origin is at most 4. Write the constraints as inequalities.
Example 4
hardA triangle has sides a, b, c with perimeter 30. Write all the geometric constraints (triangle inequality and perimeter) that a, b, c must satisfy, then find the maximum possible value of side a given b = c.