The midpoint of the line segment from P1 to P2 is (-7, 1). If P1=(-5, 9)​, what is P2?

Question

The midpoint of the line segment from P1 to P2 is (-7, 1). If P1=(-5, 9)​, what is P2?

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Josephine 2 weeks 2021-11-20T12:02:44+00:00 1 Answer 0 views 0

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    2021-11-20T12:04:34+00:00

    Answer:

    Therefore the coordinate of  P₂ is (-3,1)

    Step-by-step explanation:

    Mid point: The mid-point is a point from where the distance of the end points of a line segment is equal.

    The co-ordinate of mid point of (x₁,y₁)  and (x₂,y₂) is (\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )

    Here x₁= -5  and y₁= 9

    And the coordinate of the mid point is (-7,1).

    Let the coordinate of P₂ be (x,y)

    Therefore the coordinate of midpoint of P₁ and P₂ is

    (\frac{-7+x}{2} ,\frac{1+y}{2} )

    According to the problem,

    \frac{-7+x}{2} =-5

    \Rightarrow -7 +x=(-5)\times 2

    \Rightarrow -7 +x=-10

    \Rightarrow x=-10+7

    \Rightarrow x= -3    

    and          

    \frac{1+y}{2} = 1

    \Rightarrow 1+y= 1\times 2

    \Rightarrow 1+y=2

    \Rightarrow y=2-1

    \Rightarrow y=1

    Therefore the coordinate of  P₂ is (-3,1)

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