SME
Grade 10 Math · Problem type
Construct a perpendicular bisector
Use this for “AB is 6 cm and the compass is open to 4 cm. How far above AB do the arcs cross?”
Diagram
AB = 6 cm
AM = 3 cm
MP = 2.6458 cm
This is an example. Type your own values to start a new problem.
AM
=
AB
÷
2
MP
2
=
r
2
−
AM
2
Formulas
AM
=
AB
2
3
=
6
2
MP²
=
r
2
−
AM²
2.6458
2
=
4
2
−
3
2
Assumptions
•
Open the compass wider than half of AB; draw an arc from A and one from B.
•
The arcs cross at P, the same distance r from A and B. The line through P at right angles to AB bisects it at M.
•
P is MP above M, and the right triangle AMP gives MP² + AM² = r².
Step-by-step
WE KNOW
AB = 6 cm, r = 4 cm
FIND
AM (AM), MP (MP)
Step 1 · Find AM (AM)
Use AM = AB ÷ 2
M is the middle of AB.
AM
=
6
2
AM = 3 cm
Step 2 · Find MP (MP)
Use MP² = r² − AM²
The
right
triangle
AMP:
the
compass
opening
r
is
its
hypotenuse.
MP
=
√
r
2
− AM²
MP
=
√
4
2
−
3
2
MP
=
√
16 − 9
MP
=
√
7
MP = 2.6458 cm
Check
Put the numbers back in. Both sides should match.
3
=
6
2
✓
2.6458
2
=
4
2
−
3
2
✓
Topic check
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