Question

The mid point of CD is E(-1, 0). Endpoint is C(5, 2). What are the coordinates of the other endpoint

Answer 1

The coordinates of the midpoint of a line segment is the average of the coordinates of the endpoints. Calculations for the coordinates of the other endpoint are shown below.

abscissa -1 = (5 + x) / 2 ; x = -7

ordinate 0 = (2 + x) / 2 ; y = -2

Thus, the coordinates of the endpoint is (-7, -2).

Answer 2

(-7, -2)

Explanation:

The coordinates of the midpoint of a segment having the end points
`(x_1, y_1)` and
`(x_2, y_2)` are,

`((x_1+x_2)/(2), (y_1+y_2)/(2))`

Here,

`x_1 = 5\text{ and }y_1=2`

Also,

`((x_1+x_2)/(2), (y_1+y_2)/(2))=(-1,0)`

`((5+x_2)/(2), (2+y_2)/(2))=(-1,0)`

By equating the x- coordinates,

`(5+x_2)/(2)=-1`

`5+x_2=-2`

`x_2=-2-5=-7`

By equating the y- coordinates,

`(2+y_2)/(2)=0`

`2+y_2=0`

`y_2=-2`

Hence, the coordinates of the other endpoint i.e. D are,

(-7, -2)