Given that rectangle LMNO with coordinates L(0,0), M(3,0), N(3,7), O(0,7), P is the midpoint of LM⎯⎯⎯, and Q is the midpoint of NO⎯⎯⎯, which of the following proves that PQ=LO?

Answers attached

Given That Rectangle LMNO With Coordinates L(0,0), M(3,0), N(3,7), O(0,7), P Is The Midpoint Of LM, And

Answers

Answer 1

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


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