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FromTheMoon [43]
3 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]3 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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Answer:

Let's define the variables:

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This can be written as:

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"5 years from now she will be thrice as old as her daughter"

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We want to know how old is the mother five years from now.

First, our equations are:

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First, we need to isolate one of the variables in one of the equations, because for the solution we want the mother's age, we should isolate the daughter's age.

Let's isolate D in the first equation:

M/2 = D

Now we can replace this in the other equation:

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M + 5 - (3/2)*M = 0

-(1/2)*M + 5 = 0

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2*5 = M = 10

So the mother is 10 years old (this hasn't a lot of sense, maybe there is a wrong number on the question)

and 5 years from now, the mother will be:

10 + 5 = 15 years old.

8 0
3 years ago
The circle will be dilated by a scale factor of 6. What is the value for n if the expression nPI represents the circumference of
IgorLugansk [536]
A dilation by a scale factor of 6 will cause the radius to increase by a factor of 6. So r_{new} = 6r. If we plug this value of r into the formula for the circumference of a circle we get C = 2\pi r_{new} = 2\pi *6r = 12\pi r

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Answer:

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Step-by-step explanation:

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(B∩C) = {6}      [Common element in set B and set C]

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