Answer :
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