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Find the other endpoint of the line segment with the given endpoint and midpoint.

1. Endpoint: (-5, 4)
Midpoint: (-10, -6)

2. Endpoint: (-8, 8)
Midpoint: (5, -3) ​

Sagot :

PUBGxCODidn

ANSWERS:

No. 1: [tex]\large{Endpoint\:\:(\rm{-}5, 4)}[/tex]

[tex]\:\:\:\:\:\:\:\:\large{Midpoint\:\:(\rm{-}10, \rm{-}6)}[/tex]

  • [tex]\huge\tt{\underline{\green{Endpoint\:\:(\rm{-}15, \rm{-}16)}}}[/tex]

No. 2: [tex]\large{Endpoint\:\:(\rm{-}8, 8)}[/tex]

[tex]\:\:\:\:\:\:\:\:\large{Midpoint\:\:(5, \rm{-}3)}[/tex]

  • [tex]\huge\tt{\underline{\green{Endpoint\:\:(18, \rm{-}14)}}}[/tex]

[tex]\\[/tex]

SOLUTIONS:

No. 1: [tex]\large{Endpoint\:\:(\rm{-}5, 4)}[/tex]

[tex]\:\:\:\:\:\:\:\:\large{Midpoint\:\:(\rm{-}10, \rm{-}6)}[/tex]

  • [tex]\large{E = (x_2, y_2)}[/tex]

  • [tex]\large{E = (2x_m - x_1, 2y_m - y_1)}[/tex]

  • [tex]\large{E = (2(\rm{-}10) - \rm{-}5, 2(\rm{-}6) - 4)}[/tex]

  • [tex]\large{E = (2(\rm{-}10) + 5, 2(\rm{-}6) - 4)}[/tex]

  • [tex]\large{E = (\rm{-}20 + 5, \rm{-}12 - 4)}[/tex]

  • [tex]\Longrightarrow\:\:\large\green{{E = (\rm{-}15, \rm{-}16)}}[/tex]

[tex]\\[/tex]

No. 2: [tex]\large{Endpoint\:\:(\rm{-}8, 8)}[/tex]

[tex]\:\:\:\:\:\:\:\:\large{Midpoint\:\:(5, \rm{-}3)}[/tex]

  • [tex]\large{E = (x_2, y_2)}[/tex]

  • [tex]\large{E = (2x_m - x_1, 2y_m - y_1)}[/tex]

  • [tex]\large{E = (2(5) - \rm{-}8, 2(\rm{-}3)\rm{ - 8)}}[/tex]

  • [tex]\large{E = (2(5) + 8, 2(-3)-8)}[/tex]

  • [tex]\large{E = (10 + 8, -6 - 8)}[/tex]

  • [tex]\Longrightarrow\:\:\large\green{{E = (18, -14)}}[/tex]

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