Question

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 in the boxes. ( , )

Answer 1

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

Answer 2

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).