Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.
Easy: Ratios with whole-number answers
P divides AB in the ratio a : b when AP is a parts and PB is b parts, so P is a ÷ (a + b) of the way from A to B. Find that fraction, multiply it by the change in x and the change in y, and add the results to A's coordinates.
Find the coordinates of point P.
Tip: tick “Step-by-step answer key” in the generator to print each step for marking.
The point is 1 part from A and 2 parts from B, so it is 1/3 of the way from A to B. Add 1/3 of the change in x and y to A.
Yes. Partitioning from A to B in 1 : 2 gives a point near A; from B to A it gives a point near B. Always start from the first point named.
Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.
Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.
Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.