Question

The midpoint of JKis M (6, 3). One endpoint is J (14, 9). Find the coordinates of endpoint K.

Answer 1

The endpoint K (-2, -3)

Answer 2

The coordinates of endpoint K are (-2,-3)

Explanation:

Midpoint

Given two points J(jx, jy) and K(kx, ky), the coordinates of the midpoint M(mx,my) are given by:

`\displaystyle m_x=(j_x+k_x)/(2)`

`\displaystyle m_y=(j_y+k_y)/(2)`

We are given the coordinates of M and need to find the coordinates of K. From the equations above, solve for kx and ky:

`k_x=2m_x-j_x`

`k_y=2m_y-j_y`

The points are M(6,3) and J(14,9), thus:

`k_x=2\cdot 6-14=-2`

`k_y=2\cdot 3-9=-3`

The coordinates of endpoint K are (-2,-3)