M is the midpoint of JK. find the coordinates of K.
1. J (-8,4) M (-1,1)
2. J (9,-5) M (5, -2)
3. J (0,11) M (-3,2)
I hate this problem cuz instead of finding the midpoint, your finding an endpoint instead, and I don't know if midpoint formula applies if you're finding an endpoint instead.
To find the coordinates of point K, we need to determine the position of the midpoint M and use it to calculate the coordinates of K based on the rules of midpoints.
The midpoint of a line segment is the average of the coordinates of the endpoints. Therefore, we can use this information to find K.
1. J (-8,4) M (-1,1):
To find the coordinates of K, we can use the formula for finding the midpoint:
K = 2M - J
Substituting the values:
K = 2(-1,1) - (-8,4)
K = (-2,2) - (-8,4)
K = (-2+8, 2-4)
K = (6, -2)
Therefore, the coordinates of point K are (6, -2).
2. J (9,-5) M (5, -2):
Using the midpoint formula:
K = 2M - J
Substituting the values:
K = 2(5, -2) - (9, -5)
K = (10, -4) - (9, -5)
K = (10-9, -4+5)
K = (1, 1)
The coordinates of point K are (1, 1).
3. J (0,11) M (-3,2):
Applying the midpoint formula:
K = 2M - J
Substituting the coordinates:
K = 2(-3,2) - (0,11)
K = (-6,4) - (0,11)
K = (-6-0, 4-11)
K = (-6, -7)
The coordinates of point K are (-6, -7).
I'll do #2, you do the others
2.
let the endpoint be K(x,y)
(x+9)/2 = 5
x+9 = 10
x = 1
(y - 5)/2 = -2
y-5 = -4
y = 1
K is (1,1)
check:
midpoint of JK = ( (9+1)/2 , (-5+1)/2)
= (5,-2) as given