Chapter 1: Orienting Yourself: The Use of Coordinates
Chapter 1: Orienting Yourself: The Use of Coordinates
Exercise
Question
Question: 9 (i)
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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.
| S | M | T |
|---|---|---|
| (-3, 0) | (0, 0) | (3, 0) |
When M is the mid-point of ST, can you find any connection between the coordinates of M, S and T?
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Answer
1
Find the midpoint of S (-3, 0) and T (3, 0) 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 (-3, 0) and T (3, 0) is: $\left(\dfrac{-3 + 3}{2}, \dfrac{0 + 0}{2}\right)$ = (0, 0). 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.