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Pure 1 course · All short practice · Notes & examples

Maths4U Original · 9709 Pure 1

Distance, midpoint and geometric reasoning

Check a short answer, use a hint, then study the reasoning. These checks assess the final answer; use the exam-style problems to practise written explanations.

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Recall
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M4U-P1-QP-COORDINATE-GEOMETRY-DISTANCE-MIDPOINT-01

distance

Maths4U Original · Short practice

Find the distance between \((-2,1)\) and \((4,9)\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Method
Info
M4U-P1-QP-COORDINATE-GEOMETRY-DISTANCE-MIDPOINT-02

midpoint

Maths4U Original · Short practice

Find the y-coordinate of the midpoint of \((-5,8)\) and \((7,-2)\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Apply
Info
M4U-P1-QP-COORDINATE-GEOMETRY-DISTANCE-MIDPOINT-03

missing endpoint

Maths4U Original · Short practice

\(M=(2,-1)\) is the midpoint of \(A=(-3,4)\) and \(B\). Find the x-coordinate of \(B\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Check understanding
Info
M4U-P1-QP-COORDINATE-GEOMETRY-DISTANCE-MIDPOINT-04

perpendicular bisector

Maths4U Original · Short practice

Which point is equidistant from \((0,0)\) and \((6,0)\)?

Choose one answer.

Your answer

Fresh review variant
Info
M4U-P1-QP-VAR-COORDINATE-GEOMETRY-DISTANCE-MIDPOINT-01

distance

Maths4U Original · Short practice

Find the distance between \((1,-2)\) and \((6,10)\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant
Info
M4U-P1-QP-VAR-COORDINATE-GEOMETRY-DISTANCE-MIDPOINT-02

midpoint

Maths4U Original · Short practice

Find the midpoint y-coordinate for \((-4,-7)\), \((8,3)\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant
Info
M4U-P1-QP-VAR-COORDINATE-GEOMETRY-DISTANCE-MIDPOINT-03

missing endpoint

Maths4U Original · Short practice

\((4,3)\) is the midpoint of \((-1,5)\) and B. Find the x-coordinate of B.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant
Info
M4U-P1-QP-VAR-COORDINATE-GEOMETRY-DISTANCE-MIDPOINT-04

perpendicular bisector

Maths4U Original · Short practice

A point \((x,7)\) is equidistant from \((1,0)\) and \((9,0)\). Find x.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

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