The midpoint of a line divides the line into equal segments.
The option that proves PQ = LO is (a)
The given parameters are:
[tex]\mathbf{L = (0,0)}[/tex]
[tex]\mathbf{M = (3,0)}[/tex]
[tex]\mathbf{N = (3,7)}[/tex]
[tex]\mathbf{O = (0,7)}[/tex]
P is the midpoint of LM.
So, we have:
[tex]\mathbf{P = \frac{LM}{2}}[/tex]
[tex]\mathbf{P = (\frac{(0 +3}{2},\frac{0+0}{2})}[/tex]
[tex]\mathbf{P = (\frac{3}{2},0)}[/tex]
Q is the midpoint of NO.
So, we have:
[tex]\mathbf{Q = \frac{NO}{2}}[/tex]
[tex]\mathbf{Q = (\frac{(3 +0}{2},\frac{7+7}{2})}[/tex]
[tex]\mathbf{Q = (\frac{3}{2},7)}[/tex]
Distance PQ is calculated as follows:
[tex]\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
This gives:
[tex]\mathbf{PQ = \sqrt{(3/2 - 3/2)^2 + (0 - 7)^2}}[/tex]
[tex]\mathbf{PQ = \sqrt{ 7^2}}[/tex]
[tex]\mathbf{PQ = 7}[/tex]
Distance LO is calculated as follows:
[tex]\mathbf{LO = \sqrt{(0 - 0)^2 + (0 - 7)^2}}[/tex]
[tex]\mathbf{LO = \sqrt{ 7^2}}[/tex]
[tex]\mathbf{LO=7}[/tex]
So, we have:
[tex]\mathbf{PQ = 7}[/tex]
[tex]\mathbf{LO=7}[/tex]
Thus:
[tex]\mathbf{PQ = LO}[/tex]
Hence, the correct option is (a)
Read more about distance and midpoints at:
https://brainly.com/question/11231122
