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19. Elein and Naya wanted to meet between their
houses at midpoint (4,1). If Elien's house is at point
A. (7,-1.5)
(10,-4).
B. (-2,6)
Find the coordinates of Naya's house.
C. (0,0)

Sagot :

MrRoyalidn

Answer:

[tex](-2,6)[/tex]

Step-by-step explanation:

Given

[tex]Elena = (10,-4)[/tex]

[tex]Midpoint = (4,1)[/tex]

Required

Determine the coordinates of Naya's

Midpoint is calculated as:

[tex]M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)[/tex]

In this case:

[tex](x_1,y_1) = (10,-4)[/tex]

[tex](x,y) = (4,1)[/tex]

So, we have:

[tex](4,1) = \frac{1}{2}(10+x_2,-4+y_2)[/tex]

Multiply through by 2

[tex]2 * (4,1) = \frac{1}{2}(10+x_2,-4+y_2) * 2[/tex]

[tex](8,2) = (10+x_2,-4+y_2)[/tex]

By comparison:

[tex]8 = 10 + x_2[/tex]

[tex]2 = -4 + y_2[/tex]

So:

[tex]8 = 10 + x_2[/tex]

[tex]x_2 = 8 - 10[/tex]

[tex]x_2 = -2[/tex]

[tex]2 = -4 + y_2[/tex]

[tex]y_2 =2+4[/tex]

[tex]y_2 =6[/tex]

So, the coordinate is: [tex](-2,6)[/tex]

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