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)

Please help me with this! I need help on this step by step. Thank you!

I will do one of them, you do the rest using my format

1. Let K be (x,y)
then (x+(-8) )/2 = -1 and (y+4)/2 = 1
x-8 = -2 and y+4 = 2
x = 6 and y = -2
so K is (6,-2)

6,-2

(6;2)

Sure, I'd be happy to help you with this step by step! Let's go through each given scenario one by one:

1. J (-8,4) M (-1,1):
To find the coordinates of K, we can use the midpoint formula, which states that the coordinates of the midpoint M are the average of the coordinates of J and K.

Let's set up the formula using the given information:
M = (-1,1)
J = (-8,4)
K = (?, ?)

Using the midpoint formula, we can calculate the coordinates of K as follows:
(Kx, Ky) = ((Jx + Mx)/2, (Jy + My)/2)
(Kx, Ky) = ((-8 + (-1))/2, (4 + 1)/2)
(Kx, Ky) = (-9/2, 5/2)

Therefore, the coordinates of K in this scenario are (-9/2, 5/2).

2. J (9,-5) M (5, -2):
Again, let's set up the midpoint formula using the given information:
M = (5,-2)
J = (9,-5)
K = (?, ?)

Applying the midpoint formula, we get:
(Kx, Ky) = ((Jx + Mx)/2, (Jy + My)/2)
(Kx, Ky) = ((9 + 5)/2, (-5 + (-2))/2)
(Kx, Ky) = (14/2, -7/2)

So, the coordinates of K in this scenario are (7, -7/2).

3. J (0,11) M (-3,2):
Once again, we'll set up the midpoint formula using the given information:
M = (-3,2)
J = (0,11)
K = (?, ?)

Using the midpoint formula:
(Kx, Ky) = ((Jx + Mx)/2, (Jy + My)/2)
(Kx, Ky) = ((0 + (-3))/2, (11 + 2)/2)
(Kx, Ky) = (-3/2, 13/2)

Therefore, the coordinates of K in this scenario are (-3/2, 13/2).

I hope this helps! Let me know if you have any further questions.

To find the coordinates of point K, we can use the midpoint formula. The midpoint formula states that if M is the midpoint of a line segment with endpoints J and K, then the coordinates of M are given by the averages of the x-coordinates and the y-coordinates of J and K.

Let's take each given set of points and find the coordinates of K step-by-step:

1. Set J(-8,4) and M(-1,1).
- The x-coordinate of the midpoint M is (-8 + -1) / 2 = -9 / 2 = -4.5
- The y-coordinate of the midpoint M is (4 + 1) / 2 = 5 / 2 = 2.5
- Since M is the midpoint of JK, the coordinates of K are (-4.5, 2.5).

2. Set J(9,-5) and M(5, -2).
- The x-coordinate of the midpoint M is (9 + 5) / 2 = 14 / 2 = 7
- The y-coordinate of the midpoint M is (-5 + -2) / 2 = -7 / 2 = -3.5
- Since M is the midpoint of JK, the coordinates of K are (7, -3.5).

3. Set J(0,11) and M(-3,2).
- The x-coordinate of the midpoint M is (0 + -3) / 2 = -3 / 2 = -1.5
- The y-coordinate of the midpoint M is (11 + 2) / 2 = 13 / 2 = 6.5
- Since M is the midpoint of JK, the coordinates of K are (-1.5, 6.5).

Therefore, the coordinates of point K for each of the given sets are:
1. K (-4.5, 2.5)
2. K (7, -3.5)
3. K (-1.5, 6.5)

-7,3