Question

The midpoint of CD is E(-1, 0) one endpoint is C(5, 2) what are the coordinates of the other endpoint? Please show all work and steps :/

Answer 1

the coordinate for endpoint d would be (-7,-2) because the distance from point c to the midpoint e is 6 points to the left and 2 down which means is the same distance from midpoint e to point d

Answer 2

(-7,-2)

Explanation:

Given: The midpoint of CD is E(-1, 0) one endpoint is C(5, 2)

To Find: coordinates of the other endpoint

Solution:

in line segment CD,

end point C is (5,2)

let other end point D be=
`(\text{x},\text{y})`

mid point of segment CD is E, (-1,0)

We know that,

if
`( \text{x}_(2) ,\text{y}_2)` is mid point of a line segment with endpoint
`( \text{x}_(1) ,\text{y}_(1))` and
`( \text{x}_(3) ,\text{y}_(3))` , then

`\text{x}_(2) =\frac{\text{x}_(1)+\text{x}_(3)}{2}`

and

`\text{y}_(2) =\frac{\text{y}_(1)+\text{y}_(3)}{2}`

therefore putting values

`-1=\frac{5+\text{x}}{2}`

`-2=5+\text{x}`

`\text{x}= -7`

`0=\frac{2+\text{y}}{2}`

`0=2+\text{x}`

`\text{x}= -2`

therefore the coordinates of the other endpoint D are(-7,-2)