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In the diagram below, R is located at (24,0), N is located at (12,18), T is located at (12,6), and E is located at (18,15). Assume that N,K,T,E,I, and B are midpoints. Complete the following table. Vertices S K I B A Coordinates

Sagot :

MrRoyal

The midpoint of a segment divides the segment into equal halves

  • The coordinates of K are: [tex]\mathbf{K = (12,12)}[/tex]
  • The coordinates of I are: [tex]\mathbf{I = (24,24)}[/tex]
  • The coordinates of B are: [tex]\mathbf{B = ( 30,33 )}[/tex]

The given parameters are:

[tex]\mathbf{R =(24,0)}[/tex]

[tex]\mathbf{N =(12,18)}[/tex]

[tex]\mathbf{T =(12,6)}[/tex]

[tex]\mathbf{E =(18,15)}[/tex]

K is the midpoint of N and T.

So, we have:

[tex]\mathbf{K = (\frac{N_x + T_x}{2},\frac{N_y + T_y}{2})}[/tex]

This gives

[tex]\mathbf{K = (\frac{12 + 12}{2},\frac{18+ 6}{2})}[/tex]

[tex]\mathbf{K = (12,12)}[/tex]

E is the midpoint of T and I.

So, we have:

[tex]\mathbf{E = (\frac{I_x + T_x}{2},\frac{I_y + T_y}{2})}[/tex]

This gives

[tex]\mathbf{(18,15) = (\frac{I_x + 12}{2},\frac{I_y+ 6}{2})}[/tex]

Multiply through by 2

[tex]\mathbf{(36,30) = (I_x + 12,I_y+ 6)}[/tex]

By comparison

[tex]\mathbf{I_x + 12 = 36.\ I_y + 6 =30}[/tex]

So, we have:

[tex]\mathbf{I_x= 24.\ I_y =24}[/tex]

Hence, the coordinates of I are:

[tex]\mathbf{I = (24,24)}[/tex]

I is the midpoint of E and B.

So, we have:

[tex]\mathbf{I = (\frac{E_x + B_x}{2},\frac{E_y + B_y}{2})}[/tex]

This gives

[tex]\mathbf{(24,24) = (\frac{18 + B_x}{2},\frac{15 + B_y}{2})}[/tex]

Multiply through by 2

[tex]\mathbf{(48,48) = (18 + B_x,15 + B_y)}[/tex]

By comparison

[tex]\mathbf{18 + B_x = 48,\ 15 + B_y = 48 }[/tex]

So, we have:

[tex]\mathbf{B_x = 30,\ B_y = 33 }[/tex]

Hence, the coordinates of B are:

[tex]\mathbf{B = ( 30,33 )}[/tex]

Read more about midpoints at:

https://brainly.com/question/18068617

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