Page 137 - MAT KS3 Y8 Cambridge CheckPoint

13.3 The midpoint of a line segment

✦ Exercise 13.3

1 A is the point (2, 4) and B is the point (6, 0).
a Mark A and B on a coordinate grid and draw the line segment AB.
b Find the coordinates of the midpoint of AB.
y
2 Find the coordinates of the midpoint of each 4 A
side of this pentagon. 3
E 2 B
1
D
0 x
–5 –4 –3 –2 –1 1 2 3 4 5
–1
–2
C
–3

3 A is the point (8, 0), B is the point (0, 6) and C is the point (10, 12).
Find the midpoint of: Draw a diagram if
a AB b AC c BC. you want to.

4 Find the midpoint of the line segment between:
a (1, −1) and (7, 5) b (−4, −3) and (2, 5) c (10, −2) and (−2, 10).

5 Find the midpoint of the line segment between:
a (5, −2) and (2, −6) b (−4, 5) and (3, 0) c (−7, 5) and (−10, 10).
6 Find the midpoint of the line segment between:
a (20, 10) and (50, 30) b (20, 30) and (−40, −10) c (−17, 14) and (19, −20).
7 Find the coordinates of the midpoint of each side of this triangle.
y
40
30
D
20
E 10

–4 –3 –2 –1 0 1 2 3 4 x
–10
–20
–30
F
–40

8 A square has vertices at A(2, 3), B(3, −1), C(−1, −2) and D(−2, 2).
a Draw the square.
b The diagonals are AC and BD. Show that the diagonals have the same midpoint.
9 A parallelogram has vertices at P(2, 5), Q(−2, 3), R(2, −1) and S(6, 1). The diagonals are PR and QS.
Show that the diagonals have the same midpoint.

10 A quadrilateral has vertices at (−2, 1), (0, 4), (5, 2) and (1, −1). Do the diagonals have the same
midpoint? Justify your answer.

11 The midpoint of a line segment is (4, 1). One end of the line segment is (2, 5). Find the coordinates
of the other end of the line segment.
13 Graphs 135