Anyone knows about this ?.

The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

daser333 [38]

Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}$

$EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}$

$FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}$

$DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}$

Slope formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of DE,

$m_1=\frac{4-5}{2+2}= \frac{-1}{4}$

Slope of EF,

$m_2=\frac{0-4}{0-2}= 2$

Slope of FG,

$m_3=\frac{1-0}{-4-0}= \frac{-1}{4}$

Slope of DG,

$m_4=\frac{1-5}{-4+2}= 2$

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

3 0

3 years ago

Read 2 more answers

Suppose a subset of eight different days of the year is selected at random. What is the probability that each day is from a diff

goldfiish [28.3K]

Answer:

P = 0.05

Step-by-step explanation:

12 months * 30 days each = 360 days

From 306 days, we have to select 8 days = 360C8 ways(Total ways)

We want each days from different month. First, we have to select 8 month from 12 month = 12C8 ways

---By selecting 8 month, we will select a days from each month. That can be done in = 30C1 * 30C1 * .................30C1 (8 ways) [From a month with 30 days, we can select a day in 30C1 ways = 30 ways]

Therefore P = Number of ways of selecting each days from different month / Total number of ways

P = 12C8 * 30^8 / 360C8

P = 495 * 656100000000 / 6469697679132645

P = 0.0501985588982791

P = 0.05

Hence the probability that each day is from a different month is 0.05

6 0

2 years ago

1/2x+3=-1<br><br><br><br><br> HELP ASAP!!

fenix001 [56]

Step-by-step explanation:

$\frac{1}{2} x + 3 = - 1 \\ \frac{x}{3} + 3 = - 1 \\ \frac{x}{3} = - 1 - 3 \\ \frac{x}{3} = - 4 \\ x = - 4 \times 3 \\ x = - 12$

4 0

2 years ago

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Which number should each side of the equation 3/4x = 9 be multiplied by to produce the equivalent equation of x =12

S_A_V [24]

3/4x = 9....multiply both sides by 4 <==
3x = 9 * 4
3x = 36
x = 36/3
x = 12

5 0

2 years ago

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A pair of parallel lines is cut by a transversal, as shown:

liubo4ka [24]

<h3>Answer:</h3><h3 /><h2>Step-by-step explanation: the answer</h2><h2>let p' be the corresponding angle of the angle p (that is because of the prallelism and the transversal, look the image)</h2><h2>but p' and p are correspondant angles implies p'=p,</h2><h2>looking at the figure, p' and q are opposite angles</h2><h2>so q=p' and p'=p implies q=p</h2><h2>the answer is</h2><h2>p = q</h2><h2 />

8 0

2 years ago