Question

AB has endpoints A(3,6) and B(9,-2) and midpoint M. What are the coordinates of M?

a) M(6, 2)
b) M(3, 6)
c) M(9, -2)
d) M(6, 2)

Answer 1

The midpoint M of the line segment AB with ends at A(3,6) and B(9,-2) is calculated using the midpoint formula and is found to be M(6, 2), corresponding with option (a).

Step-by-step explanation:

The student has asked for the coordinates of the midpoint M of the line segment AB with endpoints A(3,6) and B(9,-2). To find the coordinates of the midpoint M, we use the midpoint formula which is M = ((x1 + x2)/2, (y1 + y2)/2). Plugging in the given coordinates, A(3,6) and B(9,-2), we calculate the midpoint as follows:

M = ((3 + 9)/2, (6 + (-2))/2)

M = (12/2, 4/2)

M = (6, 2)

Therefore, the correct coordinates of the midpoint M are (6, 2), which matches with option (a).