Ian's home is represented by the point (4, 4) on the coordinate grid. Joe's home is represented by the point (10, 6) on the coordinate grid. They want to meet at a diner is halfway between their houses (i.e., divides the line from Ian's house to Joe's house in a 1:1 ratio). What are the coordinates of the diner?Ian's home is represented by the point (4, 4) on the coordinate grid. Joe's home is represented by the point (10, 6) on the coordinate grid. They want to meet at a diner is halfway between their houses (i.e., divides the line from Ian's house to Joe's house in a 1:1 ratio). What are the coordinates of the diner?choice;(5, 3)(7, 5)(2, 2)(14, 10

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KinsleyE779759 KinsleyE779759 · Answer 1 · 2022-10-28T03:22:11+02:00

Given:

Ian's home coordinated = (4, 4)

Joe's home coordinated = ( 10, 6)

Ratio = 1:1

Find-:

The coordination of diner point

Explanation-:

Coordination of ratio point is:

Let coordination of P and Q is:

[tex]\begin{gathered} P=(x_1,y_1) \\ \\ Q=(x_2,y_2) \end{gathered}[/tex]

So point S is:

[tex]S=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]

Where,

[tex]\begin{gathered} P=(4,4) \\ \\ Q=(10,6) \\ \\ m:n=1:1 \end{gathered}[/tex]

So the dinner point is:

[tex]\begin{gathered} =(\frac{10+4}{1+1},\frac{6+4}{1+1}) \\ \\ =(\frac{14}{2},\frac{10}{2}) \\ \\ =(7,5) \end{gathered}[/tex]

Dinner point is: (7,5)