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

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).

Answer 2

(11,16)

Explanation:

Hello

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

`P1(x_(1),y_(1) )\\P2(x_(2),y_(2))\\\\Midpoint((x_(1)+x_(2))/(2), (y_(1)+y_(2))/(2))\\`

Step 1

Let

P1=J(5,-6)

Midpoint=M(8,5)

P2=k=?

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

Step 2

solve for X(2)

`8=(5+x_(2))/(2)\ \\\ \\\\8*2=5+x_(2) \\16-5=x_(2) \\x_(2) =11`

Step 3

solve for y(2)

`5=(-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