Loci: a fixed distance from a line or shape
The Maths Habit
Sam draws all the points 1 cm from the rectangle, outside it. Sam gives the drawing square corners. Is Sam right?
No. Sam's corner is more than 1 cm away. Each corner is an arc.
- Line segment
- A straight line with two ends.
- Locus
- All the points that follow a rule.
- Parallel
- Always the same distance apart.
From a line segment
- Straight sides: parallel to the segment, the distance away.
- Round ends: an arc about each end, radius the distance.
From a shape
- Straight sides: parallel to each side.
- Outside: round corners, an arc about each corner.
- Inside: square corners.
What shape are the ends?
How long is the whole shape?
Draw the locus of points that are 2 cm from the line segment AB. Straight sides, then round ends
Draw the locus of points that are 1.5 cm from CD. The straight sides are drawn. Round ends, radius 1.5 cm
Draw the locus of points that are 2 cm from the line segment AB. Straight sides, then round ends
Draw the locus of points that are 2 cm from EF. Straight sides, then round ends
Where on a rectangle do most mistakes happen?
At the corners. Outside: round them with an arc. Inside: they stay square.
Round or square corners?
Draw the locus of points outside the rectangle that are 1 cm from it. Round corners
Draw the locus of points inside the rectangle that are 1.5 cm from it. Square corners
Draw the locus of points outside the rectangle that are 1 cm from it. Round corners
Draw the locus of points outside the triangle that are 1 cm from it. Round corners, an arc at each
Draw the locus of points that are 2 cm from the line segment AB. Straight sides, then round ends
Draw the locus of points that are 1.5 cm from the line segment PQ. Straight sides, then round ends
Draw the locus of points outside the rectangle that are 1 cm from it. Round corners
Draw the locus of points inside the square that are 1 cm from it. Square corners
Draw the locus of points outside the rectangle that are 1 cm from it. Round corners
Draw the locus of points outside the triangle that are 1.5 cm from it. Round corners, an arc at each
Answer sheet
Thumbs up if it is right. Thumbs down if it is wrong.
All the points 2 cm from a line segment make a rectangle.
WrongInside a rectangle, the locus has square corners.
RightOutside a triangle, there is an arc at each corner.
RightThe round ends have a radius of the distance.
Right
A dog is on a 5 m lead that slides along a 10 m rail. How long and how wide is the region it can reach?
20 m by 10 mShade the points less than 2 cm from a line segment AB and more than 2 cm from its midpoint.
Track minus circleKai says the locus of points 1 cm from a square is a bigger square. Explain why Kai is wrong.
Corners are arcs
Draw the locus of points one square away from the line AB.
Straight sides, round endsAB is 7 cm. How long, end to end, is the locus of points 2 cm from AB?
11 cmSam: 1 cm outside, square corners. Right?
Arcs: the corner is too far