Cambridge IGCSE · Mathematics (0580)

Length and midpoint: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Length and midpoint.

10 questions27 marksFree, no account

Question 1

1 mark

In a coordinate plane, point \(P\) has coordinates \((-4, 2)\) and point \(Q\) has coordinates \((2, 10)\).
Calculate the distance between point \(P\) and point \(Q\).

Question 2

1 mark

The midpoint of the line segment joining \(A(x, 5)\) and \(B(6, y)\) is \(M(4, 2)\).
Find the values of \(x\) and \(y\).

Question 3

1 mark

A square \(ABCD\) has vertices \(A(1, 1)\) and \(C(5, 5)\) as opposite corners.
Find the coordinates of the center of the square and the length of one side of the square.

Question 4

1 mark

A line segment connects the points \(A(2, 7)\) and \(B(8, -1)\).
Find the coordinates of the midpoint of the line segment \(AB\).

Question 5

1 mark

The gradient of a line segment joining point \(A(1, 2)\) and point \(B(5, p)\) is \(\frac{3}{4}\).
Calculate the length of the line segment \(AB\).

Question 6

2 marks

Point A has coordinates \((7, -2)\) and point B has coordinates \((-3, 6)\). Calculate the coordinates of the midpoint of the line segment AB.

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Question 7

4 marks

A triangle has vertices at \(A(1, 2)\), \(B(1, 6)\), and \(C(4, 2)\). Calculate the perimeter of triangle ABC.

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Question 8

5 marks

The point \(M(5, 4)\) is the midpoint of the line segment \(AB\). Point \(A\) has coordinates \((2, k)\) and the length of the line segment \(AB\) is \(10\) units. Find the two possible values of \(k\).

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Question 9

4 marks

The coordinates of two points are A \((-2, 5)\) and B \((4, 11)\).
(a) Find the coordinates of the midpoint, M, of the line segment AB.
(b) Calculate the exact length of the line segment AB.
(c) Point C lies on the same line such that B is the midpoint of AC. Find the coordinates of C.

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Question 10

7 marks

The points A and B have coordinates \((3, 2)\) and \((6, 6)\) respectively.
(a) Calculate the length of the line segment AB.
(b) Find the coordinates of the midpoint of AB.
(c) Point C lies on the y-axis such that the distance AC is equal to the distance AB. Find the possible coordinates for point C.

Write your answer out first, then check it against the worked solution.

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