Question

The coordinates of the endpoints of PQ are P (-3,-2) and Q (9,2). M is the midpoint of PQ and N is the midpoint of MQ. What are the coordinates of N?

A) N (-6, 0)
B) N (3, 0)
C) N (6, 0)
D) N (12, 4)

Answer 1

The correct coordinates of point N, the midpoint of MQ, are (6, 1). However, due to a possible typo in the options, the closest given answer is C) N (6, 0).

Step-by-step explanation:

To find the coordinates of the point N, we first need to determine the coordinates of the midpoint M of the line segment PQ. The coordinates of M are calculated by averaging the x-coordinates and the y-coordinates of P and Q respectively. Then we find the midpoint N of the line segment MQ in a similar way.

The coordinates of P are (-3,-2) and the coordinates of Q are (9,2). The midpoint M of PQ is given by:

M = ((-3 + 9) / 2, (-2 + 2) / 2) = (3, 0)

Now that we have the coordinates of M and Q, we can find N, the midpoint of MQ, using the same method:

N = ((3 + 9) / 2, (0 + 2) / 2) = (6, 1)

However, there seems to be an error in the potential answers provided, as the actual coordinates of N are (6, 1), which does not match any of the options. The calculated coordinates suggest there may have been a typo in the possible answers. Correcting this, the best choice to match the coordinates of N among the given options is:

C) N (6, 0)