Reach for the Star

Constructions and loci · Optional extension

L028 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

Construct the perpendicular bisector of an 8 cm segment. How far is its midpoint from either endpoint?

Reveal a worked check after attempting

4 cm; every point on the bisector is equidistant from endpoints.

Deep challenge

A point is 3 cm from A and 4 cm from B. Describe the intersection of its loci.

Reveal a worked check after attempting

Intersections of circles centred A radius 3 cm and B radius 4 cm, if the circles meet; up to two points.

Recall & Review: feedback and extension integration

Lesson L028: Constructions and loci

Objective: Use ruler and compass constructions and interpret loci as sets of points satisfying distance conditions.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.

Even Better If (EBI)

I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.

Stretch and deep challenge

Stretch: Construct the perpendicular bisector of an 8 cm segment. How far is its midpoint from either endpoint?

Deep challenge: A point is 3 cm from A and 4 cm from B. Describe the intersection of its loci.