Answer:
(14, - 13 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ (x₁ + x₂ ), (y₁ + y₂ ) ]
let (x₁, y₁ ) = (- 2, - 7) and (x₂, y₂ ) = (x, y)
Using the midpoint formulae equate to the coordinates of the midpoint.
(- 2 + x) = 6 ( multiply both sides by 2 )
- 2 + x = 12 ( add 2 to each side )
x = 14
and
(- 7 + y ) = - 10 ( multiply both sides by 2 )
- 7 + y = - 20 ( add 7 to both sides )
y = - 13
Thus
coordinates of other endpoint = (14, - 13 )
I hope this helped. I factored everything down, wrote it a different way, and got this.
Answer: w = 110° x = 83° y = 87° z = 97°
<u>Step-by-step explanation:</u>
∠(x - 13) and ∠w form a linear pair so their sum is equal to 180°
x - 13 + w = 180 → w = -x + 193
∠(x + 10) and ∠y form a linear pair so their sum is equal to 180°
x + 10 + y = 180 → y = -x + 170
∠x and ∠z form a linear pair so their sum is equal to 180°
x + z = 180 → z = 180 - x
∠x and ∠y and ∠w are the angles of a triangle so their sum equals 180°
x + y + w = 180
x + (-x + 170) + (-x + 193) = 180 Substitution
-x + 263 = 180 Add Like Terms
-x = -83 Subtracted 263 from both sides
x = 83 Divided both sides by -1
w = -x + 193 y = -x + 170 z = 180 - x
w = -83 + 193 y = -83 + 170 z = 180 - 83
w = 110 y = 87 z = 97