Chapter 1: Orienting Yourself: The Use of Coordinates

Exercise

Question

Question: 9 (ii)

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The following table shows the coordinates of points S, M and T. In each case, state whether M is the midpoint of segment ST? Justify your answer.

SMT
(2, 3)(3, 4)(4, 5)

When M is the mid-point of ST, can you find any connection between the coordinates of M, S and T?

Answer

1
Find the midpoint of S (2, 3) and T (4, 5) by averaging their x and y coordinates.Note: The midpoint of (x_1, y_1) and (x_2, y_2) is: (\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2})
Answer: Yes. M is the midpoint of ST.
\textbf{Reason: The midpoint of S (2, 3) and T (4, 5) is: $\left(\dfrac{2 + 4}{2}, \dfrac{3 + 5}{2}\right)$ = (3, 4). These coordinates are the same as the given coordinates of M. Therefore, M is the midpoint of ST.}
2
Compare each coordinate of M with the corresponding coordinates of S and T. What relationship do you notice?
Answer: The x-coordinate and y-coordinate of M are the averages of the corresponding coordinates of S and T.
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