Use the diagram below for the following question.
P(2,1), Q(11,1), and R(8,7)
M and N are the midpoints ofandrespectively.
Find the coordinates of M and N.
(its a triangle)
GIVEN: P(2 , 1) , Q(11, 1) , R(8 , 7).
(PQ)^2 = (11 - 2)^2 + (1 - 1)^2 = 81.
PQ = sqrt(81) = 9.
(QR)^2 = (8 - 11)^2 + (7 - 1)^2 = 45.
QR = sqrt(45) = 6.71.
Mid-point of PQ: XO = (2 + 11) / 2 =6.5
Yo = (1 + 1) / 2 = 1. M(6.5 , 1).
Mid-point of QR: Xo = (11 + 8) / 2 = 9.5. Yo = (1 + 7) / 2 = 4, N(9.5 , 4).
rtyityi
To find the coordinates of the midpoints M and N, we first need to calculate the average of the x-coordinates and the average of the y-coordinates of the given points.
Let's start with point P(2,1):
The x-coordinate of M is the average of the x-coordinates of points P and Q. So we add the x-coordinates of P and Q and divide by 2:
Mx = (2 + 11) / 2 = 13 / 2 = 6.5
The y-coordinate of M is the average of the y-coordinates of points P and Q. So we add the y-coordinates of P and Q and divide by 2:
My = (1 + 1) / 2 = 2 / 2 = 1
Therefore, the coordinates of M are (6.5, 1).
Moving on to point R(8,7):
The x-coordinate of N is the average of the x-coordinates of points P and R. So we add the x-coordinates of P and R and divide by 2:
Nx = (2 + 8) / 2 = 10 / 2 = 5
The y-coordinate of N is the average of the y-coordinates of points P and R. So we add the y-coordinates of P and R and divide by 2:
Ny = (1 + 7) / 2 = 8 / 2 = 4
Therefore, the coordinates of N are (5, 4).
In summary:
Coordinates of M: (6.5, 1)
Coordinates of N: (5, 4)