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maria [59]
3 years ago
15

M(8, 5) is the midpoint of JK. The coordinates of point J are (5, −6) . What are the coordinates of point K? Enter your answer i

n the boxes. ( , )
Mathematics
2 answers:
kkurt [141]3 years ago
8 0

Answer:

(11,16)

Step-by-step explanation:

Hello

if you have two points , the midpoint is given by:

P1(x_{1},y_{1} )\\P2(x_{2},y_{2})\\\\Midpoint(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})\\

Step 1

Let

P1=J(5,-6)

Midpoint=M(8,5)

P2=k=?

Midpoint(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})\\so\\\\M(8,5)=(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})\\\\Hence\\8=\frac{x_{1}+x_{2}}{2}\ and\ 5=\frac{y_{1}+y_{2}}{2}\\now\ replacing\ P1\\\\\\P1=J(5,-6)\\x_{1}=5\\y_{1}=-6\\  8=\frac{5+x_{2}}{2}\ \\\ 5=\frac{-6+y_{2}}{2}\\

Step 2

solve for X(2)

8=\frac{5+x_{2}}{2}\ \\\ \\\\8*2=5+x_{2} \\16-5=x_{2} \\x_{2} =11

Step 3

solve for y(2)

5=\frac{-6+y_{2}}{2}\\5*2=-6+y_{2}\\10+6=y_{2}\\y_{2}=16

Hence the coordinates are

K(11,16)

Have a good day

Mice21 [21]3 years ago
6 0
Let the coords of K be (x,y).
The midpoint is the average of the coords of the endpoint. So 8=(5+x)/2, making x=11. And 5=(-6+y)/2 making y=16.
So K is (11,16).
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