Question

A line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm, and ym. Use the result to find the coordinates of the endpoint (x2, y2) of each line segment with the given endpoint (x1, y1) and endpoint (xm, ym).

(a)

(x1, y1) = (1, −4), (xm, ym) = (2, −1)

(x2, y2)=


(b)

(x1, y1) = (−9, 19), (xm, ym) = (5, 6)

(x2, y2)=

Answer 1

D is the Right answer got it right on test and teacher said it was right

Explanation:

Ym

Answer 2

Answer: (a) (
`x_(2),y_(2)`) = (3,2)

(b) (
`x_(2),y_(2)`) = (19,-7)

Explanation: Midpoint of a segment is halfway between 2 endpoints. It is calculated using the formulas:

`x_(m)=(x_(1)+x_(2))/(2)`

`y_(m)=(y_(1)+y_(2))/(2)`

Isolating
`x_(2)`:

`2x_(m)=x_(1)+x_(2)`

`x_(2)=2x_(m)-x_(1)`

And
`y_(2)`:

`2y_(m)=y_(1)+y_(2)`

`y_(2)=2y_(m)-y_(1)`

(a) Replacing values and calculating
`x_(2)`:

`x_(2)=(2*2)-1`

`x_(2)=3`

Calculating
`y_(2)`:

`y_(2)=[2*(-1)]-(-4)`

`y_(2)=2`

`(x_(2),y_(2))=(3,2)`

(b)
`x_(2)=(2*5)-(-9)`

`x_(2)=19`

`y_(2)=(2*6)-19`

`y_(2)` = -7

`(x_(2),y_(2))=(19,-7)`