Distance at work

Use the distance formula to check lines, circles and squares.

Distance can answer questions about shapes. The end of the chapter uses it in four ways.

1. Are three points on one line? (Problems 6 and 7, enrichment) If B is between A and C on a straight line, the two short pieces add up exactly: AB + BC = AC. If AB + BC is more than AC, the path bends at B, and the three points make a triangle instead.

2. Is a point on a circle? (Problem 12, enrichment) A circle centred at O is every point at one fixed distance, the radius, from O.

Same distance as the radius: on the circle.
Closer: inside.
Farther: outside.

3. Do two circles meet? (Problem 15) Find the distance between the two centres. If it is less than the two radii added together (and more than their difference), the circles cross.

4. Is it a square? (Problem 16) Four equal sides make a rhombus. If the two diagonals are equal as well, the rhombus is a square.

Short pieces that add up exactly mean a straight line; equal distances from a centre mean a circle.

Compare the distance between the centres with the sum of the radii.

Practise this lesson

Questions that get harder as you improve, a Tutor that helps without giving the answer away, and progress you can see. Free for every learner.

Try it now Sign up free I have an account

No account, no email address. Opens the real product.