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The co-ordinate diagram below shows two points A and B - Leaving Cert Mathematics - Question 4(a) - 2021

Question 4(a)

The co-ordinate diagram below shows two points A and B. A = (6, 2) B = (-2, -4) (ii) Find the co-ordinates of the midpoint of [AB].

Worked Solution & Example Answer:The co-ordinate diagram below shows two points A and B - Leaving Cert Mathematics - Question 4(a) - 2021

Step 1

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Answer

The coordinates of point A are $A = (6, 2)$ and the coordinates of point B are $B = (-2, -4)$ .

Step 2

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Answer

To find the midpoint M of the line segment connecting points A and B, use the midpoint formula:

$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Substituting the coordinates of A and B:

$M = \left( \frac{6 + (-2)}{2}, \frac{2 + (-4)}{2} \right) \rightarrow M = \left( \frac{4}{2}, \frac{-2}{2} \right) = (2, -1)$

The co-ordinates of the midpoint [AB] are $M = (2, -1)$ .

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