Question

Janie was given (-2,3) as the endpoint of a line segment and (1,0) as its midpoint. Which ordered pair should Janie choose as the other endpoint?

A. (-1/2, 3/2)
B. (1/2, 1/2)
C. (-5,6)
D. (4,-3)

Answer 1

`(-2+x)/(2)=1`∧
`(3+y)/(2) =0`⇔
`x = 4` ∧
`y = -3`
R: D (4, -3)

Answer 2

The other endpoint

`(x_(2) , y_(2)) is (4,-3)`

Explanation:

Given

Point 1 (-2,3)

Midpoint = (1,0)

We're to calculate the other end point.

To solve this, we'll make use of the formula of midpoints of line

Given that two lines of coordinates
`P(x_(1) ,y_(1) )` and
`Q(x_(2) ,y_(2) )`

`(m_(1),m_(2)) = (((x_(1) + x_(2) ))/(2) ,((y_(1) + y_(2) ))/(2))\\Where\\m_(1) = ((x_(1) + x_(2) ))/(2) \\and\\m_(2) = ((y_(1) + y_(2) ))/(2))\\`

From the question, we have

`m_(1) = 1\\m_(2) = 0\\x_(1) = -2\\y_(1) = 3\\`

Calculating
`x_(2)`...

From
`m_(1) = ((x_(1) + x_(2) ))/(2)`

By Substitution, we have

`1 = (-2+x_(2) )/(2) \\2 = -2+x_(2)\\2 + 2 = x_(2)\\ x_(2) = 4`

Calculating
`y_(2)`...

From
`m_(2) = ((y_(1) + y_(2) ))/(2)`

By Substitution, we have

`0 = (3+y_(2) )/(2) \\0 = 3+y_(2)\\0 - 3 = y_(2)\\ y_(2) = -3`

Hence, the other endpoint

`(x_(2) , y_(2)) is (4,-3)`