Constructing a perpendicular through a point
The Maths Habit
A swimmer at S wants to reach the straight edge of the pool as quickly as possible. Which route: a, b or c?
b. The route at right angles to the edge is the shortest.
- Perpendicular
- At right angles.
- Line segment
- A straight line with two ends.
- Shortest distance
- The length of the perpendicular from a point to a line.
From a point P to a line
- Arc from P that cuts the line twice.That makes a line segment.
- Bisect the segment: arcs from each end, the same width.
- Join P to where they cross.
At a point P on a line
- Arcs either side of P, the same width.That makes a segment with P in the middle.
- Bisect the segment.
- Join P to where the arcs cross.
How many times must the first arc cut the line?
What do you do with the segment you have made?
Construct the perpendicular from P to the line AB. Make a segment, then bisect it
Construct the perpendicular from P to the line AB. The first arc is drawn. Bisect the segment
Construct the perpendicular from P to the line AB. Make a segment, then bisect it
Construct the perpendicular from P to the line AB. The first arc is drawn. Bisect the segment
P is on the line. How can you make a segment with P exactly in the middle?
Arcs either side of P with the same width. Then bisect that segment.
Construct the perpendicular to AB at the point P. Arcs either side of P, then bisect
Construct the perpendicular to AB at P. The arcs either side are drawn. Bisect the segment
Construct the perpendicular to AB at the point P. Arcs either side of P, then bisect
Construct the perpendicular to AB at P. The arcs either side are drawn. Bisect the segment
Construct the perpendicular to AB at the point P. Arcs either side of P, then bisect
Construct the perpendicular to AB at the point P. Arcs either side of P, then bisect
Construct the perpendicular from P to the line AB. Make a segment, then bisect it
Construct the perpendicular from P to the line AB. Make a segment, then bisect it
Construct the perpendicular to AB at the point P. Arcs either side of P, then bisect
Construct the perpendicular to AB at the point P. Arcs either side of P, then bisect
Answer sheet
Thumbs up if it is right. Thumbs down if it is wrong.
The shortest way from a point to a line is at right angles to it.
RightFrom a point, the first arc only needs to touch the line once.
Wrong: twiceAt a point, the arcs either side of P must be the same width.
RightA perpendicular is any line that crosses another.
Wrong
A boat is at B. The shore is straight. Construct the shortest route to the shore.
PerpendicularConstruct a rectangle 7 cm by 4 cm, using compasses for the right angles. Measure a diagonal.
8.1 cmDraw a triangle. Construct the perpendicular from the top corner to the base. What is it?
Its height
Construct the perpendicular at P.
A line at 90° through PConstruct the perpendicular from P to the line.
A line from P at 90°Which route from Q is the shortest? Why?
b, it is perpendicular