Track quiz
Keep this table open while you work.
| Idea | How it goes |
|---|---|
| The distance formula | Square both gaps. Add them. Take the square root. |
| Counting hops | Make m + n equal hops. Walk m of them from the first point. |
| The section formula | B's numbers carry m. A's numbers carry n. Both sit over m + n. |
| Reading the ratio back | Compare the across gaps and the up gaps. Both must give the same ratio. Skip a pair of gaps that are both 0. |
| The midpoint | Average each coordinate. It is the ratio 1 : 1. |
| The missing corner | D = A + C − B, because the diagonals share one midpoint. |
| Cutting into thirds | Two points, at 1 : 2 and 2 : 1. |
| Equally far | Set the two squared distances equal. |
| Name the shape | Find every distance. Compare them. The pattern names the shape. |
What is the distance between (−1, 1) and (4, 13)?
A cut is made at 3 : 2 counted from A. How many equal hops are left to B?
Which point cuts A(1, 3) to B(7, 9) in the ratio 1 : 2?
P(3, 4) lies on A(1, 2) to B(9, 10). What is AP : PB?
What is the midpoint of A(−4, 1) and B(4, 7)?
Three corners of parallelogram ABCD are A(1, 1), B(5, 1) and C(5, 4). Where is D?
Which pair are the points of trisection of (0, 0) to (6, 12)?
Which point on the x-axis is equally far from (1, 2) and (3, 4)?
A triangle has squared sides 13, 13 and 8. What is it?
Opposite sides are 5 and 3. Both diagonals are √34. What shape is it?
P(0, 0), Q(1, 1) and R(4, 4). Do they lie on one line?
A(1, 0), B(3, 1), C(2, 3) and D(0, 2) are in order. Which is true?
This is Chapter 7, Coordinate Geometry. You now have the formulas this chapter uses.
Next: Introduction to Trigonometry. Right triangles stand up on their own.