Question

The midpoint of jk jk is m(6, 3)m(6, 3). one endpoint is j(14, 9)j(14, 9). find the coordinates of endpoint k

Answer 1

In general if we have two end points as and

So we can find mid point of these two points by using below formula as

x - co-ordinate of mid point is

y - co-ordinate of midpoint is

So in given question let co-ordinate of point k is (a , b).

Co-ordinate of j is given as (14 , 9)

So we can find x co-ordinate of midpoint of jk is

Where and

x co-ordinate of midpoint is given as x = 6

We can find y co-ordinate of jk as

Where and

y co-ordinate of midpoint is 3.

SO co-ordinate of k point is (-2 , -3).

Explanation:

Answer 2

In general if we have two end points as
`(x_1 , y_1)` and
`(x_2 , y_2)`

So we can find mid point of these two points by using below formula as

x - co-ordinate of mid point is

`x = (x_1+x_2)/(2)`

y - co-ordinate of midpoint is

`y = (y_1+y_2)/(2)`

So in given question let co-ordinate of point k is (a , b).
Co-ordinate of j is given as (14 , 9)

So we can find x co-ordinate of midpoint of jk is

`x = (x_1+x_2)/(2)`
Where
`x_1 = 14` and
`x_2 = a`
x co-ordinate of midpoint is given as x = 6


`6 = (14+ a)/(2)`

`12 = 14 + a`

`a = 12-14 = -2`

We can find y co-ordinate of jk as

`y = (y_1+y_2)/(2)`

Where
`y_1 = 9` and
`y_2 = b`
y co-ordinate of midpoint is 3.

`3 = (9+b)/(2)`

`6 = 9+ b`

`b = 6-9 = -3`

SO co-ordinate of k point is (-2 , -3).