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
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.
To find the length of MN, we need to calculate the distance between the coordinates of points M and N.
Given:
A = (1, 5)
B = (9, 7)
C = (7, 13)
To find the midpoint of AB, we can use the midpoint formula:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
Using A and B:
M = ((1 + 9) / 2, (5 + 7) / 2)
M = (10 / 2, 12 / 2)
M = (5, 6)
To find the midpoint of BC, we can use the midpoint formula:
N = ((x1 + x2) / 2, (y1 + y2) / 2)
Using B and C:
N = ((9 + 7) / 2, (7 + 13) / 2)
N = (16 / 2, 20 / 2)
N = (8, 10)
Now, we can calculate the distance between points M and N using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using M(5, 6) and N(8, 10):
d = sqrt((8 - 5)^2 + (10 - 6)^2)
d = sqrt(3^2 + 4^2)
d = sqrt(9 + 16)
d = sqrt(25)
d = 5
Therefore, the length of MN is 5.
To find the length of MN, we first need to find the coordinates of point M and point N.
Given that A has the coordinates (1, 5), B has the coordinates (9, 7), and C has the coordinates (7, 13), we can calculate the coordinates of M and N as the midpoints of line segments AB and BC, respectively.
To find the midpoint of a line segment, we need to average the x-coordinates of the endpoints and average the y-coordinates of the endpoints.
Calculating the coordinates of M:
X-coordinate of M = (X-coordinate of A + X-coordinate of B) / 2
= (1 + 9) / 2
= 5
Y-coordinate of M = (Y-coordinate of A + Y-coordinate of B) / 2
= (5 + 7) / 2
= 6
Therefore, the coordinates of point M are (5, 6).
Calculating the coordinates of N:
X-coordinate of N = (X-coordinate of B + X-coordinate of C) / 2
= (9 + 7) / 2
= 8
Y-coordinate of N = (Y-coordinate of B + Y-coordinate of C) / 2
= (7 + 13) / 2
= 10
Therefore, the coordinates of point N are (8, 10).
Now that we have the coordinates of M and N, we can calculate the length of MN using the distance formula:
Distance MN = √[(X2 - X1)² + (Y2 - Y1)²]
Substituting the coordinates of M and N, we get:
Distance MN = √[(8 - 5)² + (10 - 6)²]
= √[3² + 4²]
= √[9 + 16]
= √25
= 5
Therefore, the length of MN is 5.