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FromTheMoon [43]
2 years ago
11

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

Mathematics
1 answer:
Elina [12.6K]2 years ago
8 0

The midpoint of a line divides the line into equal segments.

The option that proves PQ = LO is (a)

The given parameters are:

\mathbf{L = (0,0)}

\mathbf{M = (3,0)}

\mathbf{N = (3,7)}

\mathbf{O = (0,7)}

P is the midpoint of LM.

So, we have:

\mathbf{P = \frac{LM}{2}}

\mathbf{P = (\frac{(0 +3}{2},\frac{0+0}{2})}

\mathbf{P = (\frac{3}{2},0)}

Q is the midpoint of NO.

So, we have:

\mathbf{Q = \frac{NO}{2}}

\mathbf{Q = (\frac{(3 +0}{2},\frac{7+7}{2})}

\mathbf{Q = (\frac{3}{2},7)}

Distance PQ is calculated as follows:

\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}

This gives:

\mathbf{PQ = \sqrt{(3/2 - 3/2)^2 + (0 - 7)^2}}

\mathbf{PQ = \sqrt{ 7^2}}

\mathbf{PQ = 7}

Distance LO is calculated as follows:

\mathbf{LO = \sqrt{(0 - 0)^2 + (0 - 7)^2}}

\mathbf{LO = \sqrt{ 7^2}}

\mathbf{LO=7}

So, we have:

\mathbf{PQ = 7}

\mathbf{LO=7}

Thus:

\mathbf{PQ = LO}

Hence, the correct option is (a)

Read more about distance and midpoints at:

brainly.com/question/11231122

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If SV⊥RT, m∠RSU = (17x – 3)°, and m∠UST = (6x – 1)°, find TSV
goblinko [34]

Applying the linear pair theorem, the measure of angle TSV in the image given is: 86°.

<h3>How to Apply the Linear Pair Theorem?</h3>

Given the following angles in the image above:

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Measure angle UST = (6x – 1)°

To find the measure of angle TSV, we need to find the value of x in the given expressions as shown below:

m∠RSU + m∠UST = 180 degrees (linear pair]

Substitute the values

17x - 3 + 6x - 1 = 180

Solve for x

23x - 4 = 180

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m∠TSV = 180 - 2(m∠UST) [Linear Pair Theorem]

m∠TSV = 180 - 2(6x - 1)

Plug in the value of x

m∠TSV = 180 - 2(6(8) - 1)

m∠TSV = 86°

Therefore, applying the linear pair theorem, the measure of angle TSV in the image given is: 86°.

Learn more about the linear pair theorem on:

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Answer:

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Step-by-step explanation:

Using the basic equation of a line:

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Substitute in (i) above

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