Question
Abc has vertices a 1 5 b 9 7 and c 7 13 m is the mid point of ab and n is the midpoint of bc which of the following is the length of mn
Answers
GPT 3.5
To find the midpoint of a line segment, we average the coordinates of its endpoints.
The coordinates of M, the midpoint of AB, are the average of the coordinates of A(1, 5) and B(9, 7):
M = ((1 + 9) / 2, (5 + 7) / 2) = (5, 6)
Similarly, the coordinates of N, the midpoint of BC, are the average of the coordinates of B(9, 7) and C(7, 13):
N = ((9 + 7) / 2, (7 + 13) / 2) = (8, 10)
Now, we can find the length of MN using the distance formula:
Length of MN = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((8 - 5)^2 + (10 - 6)^2)
= sqrt(3^2 + 4^2)
= sqrt(9 + 16)
= sqrt(25)
= 5
Therefore, the length of MN is 5.
The coordinates of M, the midpoint of AB, are the average of the coordinates of A(1, 5) and B(9, 7):
M = ((1 + 9) / 2, (5 + 7) / 2) = (5, 6)
Similarly, the coordinates of N, the midpoint of BC, are the average of the coordinates of B(9, 7) and C(7, 13):
N = ((9 + 7) / 2, (7 + 13) / 2) = (8, 10)
Now, we can find the length of MN using the distance formula:
Length of MN = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((8 - 5)^2 + (10 - 6)^2)
= sqrt(3^2 + 4^2)
= sqrt(9 + 16)
= sqrt(25)
= 5
Therefore, the length of MN is 5.