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

To find the midpoint M of the segment [AB], we can use the midpoint formula:

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

where (x1, y1) are the coordinates of point A, and (x2, y2) are the coordinates of point B.

Substituting the values we found:

• For A: (x1, y1) = (6, 2)
• For B: (x2, y2) = (-2, -4)

We substitute into the formula:

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

Calculating each component:

• For the x-coordinate: $M_x = \frac{6 + (-2)}{2} = \frac{4}{2} = 2$
• For the y-coordinate: $M_y = \frac{2 + (-4)}{2} = \frac{-2}{2} = -1$

Therefore, the co-ordinates of the midpoint [AB] are:

M = (2, -1)