Coordinates encode position, so a final answer should make geometric sense. A midpoint lies halfway between endpoints, and a point dividing a segment internally lies inside it. Use these facts to catch arithmetic and ratio-order errors.
Curriculum checked 2 October 2026 · original practice for selected skills.
You will need: Signed subtraction, squares and square roots.
Attempt each task before opening a hint. If you need help, reveal the first hint, then the setup, then compare your written steps with the solution. Finish with the retests without referring back.
Distance comes from horizontal and vertical differences. Squaring makes each contribution non-negative.
The midpoint averages corresponding coordinates; it does not average x with y.
For AP:PB=m:n, the internal point is ((nxA+mxB)/(m+n), (nyA+myB)/(m+n)). The coefficient of B is the first ratio number because increasing AP moves the point towards B.
Subtract corresponding coordinates.
The differences are 6 and 8.
The displacement forms perpendicular legs of lengths 6 and 8.
√100=10.
Answer: 10 units
Before moving on: can you explain why your method works, as well as give the answer?
Write a method as well as an answer. The tasks change the reasoning, not just the numbers.
Average x coordinates and y coordinates separately.
x=(−4+6)/2, y=(3+7)/2.
2/2=1.
10/2=5.
Answer: (1,5)
Before moving on: can you explain why your method works, as well as give the answer?
P is one-third of the way from A to B.
Multiply the displacement (9,6) by 1/3.
AP is 1 out of 3 total parts.
One-third of (9,6) is (3,2).
Answer: P=(3,2)
Before moving on: can you explain why your method works, as well as give the answer?
The horizontal coordinates are identical.
Only the vertical difference contributes.
5−(−2)=7.
The length is the non-negative magnitude.
Answer: 7 units
Before moving on: can you explain why your method works, as well as give the answer?
A tempting claim: “Use the ratio numbers as weights on the same named endpoints.”
This reverses the intended position along the segment.
These changed questions test whether you can reconstruct the method. If you use a hint, record where you got stuck and retry later. Completing this small set does not establish full chapter mastery.
Find horizontal and vertical differences.
They are 3 and 4.
9+16=25.
√25=5.
Answer: 5 units
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
Move two-thirds of the way from A.
Displacement is (6,9).
Two-thirds gives (4,6).
(2,1)+(4,6)=(6,7).
Answer: (6,7)
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
If a retest exposed the same error, rewrite the first incorrect step and explain its correction aloud. If both were independent, return to a mixed exercise or a missed paper question. A parent can ask what changed in the method rather than only asking for the answer.
No. It focuses on distance and internal division. The ratio and location checks here assume the point lies between the endpoints.
Yes. Use the two print buttons above. The question sheet leaves working space and hides solutions; the worked-solutions option includes the solution steps. Your browser can save either view as a PDF.
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