Page 136 - MAT KS3 Y8 Cambridge CheckPoint

13.3 The midpoint of a line segment

13.3 The midpoint of a line segment

The diagram shows two line segments, AB and CD.

y
A (1, 4)
4
C (–1, 3)
3
2
B (5, 2)
1
0 x
–3 –2 –1 1 2 3 4 5
–1
–2
–3
D (3, –3)

The midpoint of AB is half way between A and B. You can see from the diagram that the
midpoint of AB is (3, 3).

The midpoint of CD is (1, 0).
You can find the midpoint of a line segment by finding the means of the x-coordinates and the
y-coordinates of the end points.
+
+
 2 2 2
This gives the midpoint of AB as 15 42+ ) = (3, 3). The mean of a and b is ab .
,
+
The midpoint of CD is  –1 3 3+ – 3 ) = (1, 0).
,
2
2
Worked example 13.3
a The diagram shows points P(10, 4) and Q(−4, −6).
y
6
P (10, 4)
4
2
0 x
–8 –6 –4 –2 2 4 6 8 10
–2
–4
–6
Q (–4, –6)
Find the coordinates of the midpoint of PQ.

10 + – 4 6
a = = 3 This is the x-coordinate of the midpoint.
2 2
4 + – 6 –2
2 = 2 = –1 This is the y-coordinate of the midpoint.
The midpoint of PQ is (3, −1).

134 13 Graphs