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Kobotan [32]
2 years ago
11

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). Assu

me that N,K,T,E,I, and B are midpoints. Complete the following table. Vertices S K I B A Coordinates
Mathematics
1 answer:
julsineya [31]2 years ago
7 0

The midpoint of a segment divides the segment into equal halves

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

The given parameters are:

\mathbf{R =(24,0)}

\mathbf{N =(12,18)}

\mathbf{T =(12,6)}

\mathbf{E =(18,15)}

K is the midpoint of N and T.

So, we have:

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

This gives

\mathbf{K = (\frac{12 + 12}{2},\frac{18+ 6}{2})}

\mathbf{K = (12,12)}

E is the midpoint of T and I.

So, we have:

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

This gives

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

Multiply through by 2

\mathbf{(36,30) = (I_x + 12,I_y+ 6)}

By comparison

\mathbf{I_x + 12 = 36.\ I_y + 6 =30}

So, we have:

\mathbf{I_x= 24.\ I_y  =24}

Hence, the coordinates of I are:

\mathbf{I = (24,24)}

I is the midpoint of E and B.

So, we have:

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

This gives

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

Multiply through by 2

\mathbf{(48,48) = (18 + B_x,15 + B_y)}

By comparison

\mathbf{18 + B_x = 48,\ 15 + B_y = 48 }

So, we have:

\mathbf{B_x = 30,\  B_y = 33 }

Hence, the coordinates of B are:

\mathbf{B = ( 30,33 )}

Read more about midpoints at:

brainly.com/question/18068617

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