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Three houses A B and Clie on the same line on a map. House Blies exactly in the middle of house A and house C The point (3,6) on the

map represents house A and the point (-5-3) represents house B.

Find the coordinates of house Con the map

Respuesta :

raphealnwobi

Answer:

(-13, -12)

Step-by-step explanation:

The midpoint (x,y) between two points ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) on the coordinate plane is given by:

[tex]x=\frac{x_1+x_2}{2};\\\\y=\frac{y_1+y_2}{2}[/tex]

Hence given that house A is at (3, 6) and house B is at (-5, -3). Since house B is placed at the middle of house A and house B, let the coordinates of house C be ([tex]x_2,y_2[/tex]). Hence:

[tex]-5=\frac{3+x_2}{2\\} \\3+x_2=-10\\\\x_2=-10-3\\\\x_2=-13[/tex]

[tex]-3=\frac{6+y_2}{2\\} \\6+y_2=-6\\\\y_2=-6-6\\\\y_2=-12[/tex]

Therefore house C is at (-13, -12)

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