Answered

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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)

Sagot :

[tex] \frac{-2+x}{2}=1 [/tex]∧[tex] \frac{3+y}{2} =0[/tex]⇔[tex]x = 4[/tex] ∧[tex]y = -3[/tex]
R: D (4, -3)
MrRoyal

Answer:

The other endpoint

[tex](x_{2} , y_{2}) is (4,-3)[/tex]

Step-by-step 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 [tex]P(x_{1} ,y_{1} )[/tex] and [tex]Q(x_{2} ,y_{2} )[/tex]

[tex](m_{1},m_{2}) = (\frac{(x_{1} + x_{2} )}{2} ,\frac{(y_{1} + y_{2} )}{2})\\Where\\m_{1} = \frac{(x_{1} + x_{2} )}{2} \\and\\m_{2} = \frac{(y_{1} + y_{2} )}{2})\\[/tex]

From the question, we have

[tex]m_{1} = 1\\m_{2} = 0\\x_{1} = -2\\y_{1} = 3\\[/tex]

Calculating [tex]x_{2}[/tex]...

From [tex]m_{1} = \frac{(x_{1} + x_{2} )}{2}[/tex]

By Substitution, we have

[tex]1 = \frac{-2+x_{2} }{2} \\2 = -2+x_{2}\\2 + 2 = x_{2}\\ x_{2} = 4[/tex]

Calculating [tex]y_{2}[/tex]...

From [tex]m_{2} = \frac{(y_{1} + y_{2} )}{2}[/tex]

By Substitution, we have

[tex]0 = \frac{3+y_{2} }{2} \\0 = 3+y_{2}\\0 - 3 = y_{2}\\ y_{2} = -3[/tex]

Hence, the other endpoint

[tex](x_{2} , y_{2}) is (4,-3)[/tex]

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