Answer:
The answer to your question is:
Step-by-step explanation:
Data
M (0,0)
N (12, 0)
P (12, 16)
1.- R midpoint MN
S midpoint NP
Rx = (12 + 0)/ 2 Ry = (0 + 0) / 2
Rx = 12/2 Ry = 0
Rx = 6 Ry = 0 R ( 6, 0)
Sx = (12 + 12) / 2 Sy = (16 + 0) /2
Sx = 12 Sy = 8 S (12, 8)
2.-
slope MP = (16 - 0) / (12 - 0) = 16/12 = 4/3
slope RS = (8 - 0) / (12 - 6) = 8 / 6 = 4/3
The solpes measure the same then they are parallel
3.-
length MN = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
length MN = [tex]\sqrt{(12 - 0)^{2} + (0 - 0)^{2} }[/tex]
length MN = [tex]\sqrt{(144)^{2} }[/tex]
length MN = 12 units
length NP = [tex]\sqrt{(12 - 12)^{2} + (16 - 0)^{2} }[/tex]
length NP = [tex]\sqrt{(0)^{2} + (16)^{2} }[/tex]
length NP = [tex]\sqrt{256)^{2} }[/tex]
length NP = 16 units
length MP = [tex]\sqrt{(16 - 0)^{2} + (12 - 0)^{2} }[/tex]
length MP = [tex]\sqrt{(256) + (144)}[/tex]
length MP = [tex]\sqrt{400}[/tex]
length MP = 20 units
length RS = [tex]\sqrt{(8 - 0)^{2} + (12 - 6)^{2} }[/tex]
length RS = [tex]\sqrt{(64)} + (36)^{2} }[/tex]
length RS = [tex]\sqrt{100}[/tex]
length RS = 10 units
4.- MP is twice the length of RS (20/10)
