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3 years ago

15

Select the equation written in point-slope form.

1 answer:

slavikrds [6]3 years ago

4 0

Poin slope form is
y-y1=m(x-1)
the answer is A

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Prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.

sergiy2304 [10]

Answer:

See explanation

Step-by-step explanation:

a) To prove that DEFG is a rhombus, it is sufficient to prove that:

All the sides of the rhombus are congruent: $|DG|\cong |GF| \cong |EF| \cong |DE|$
The diagonals are perpendicular

Using the distance formula; $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$|DG|=\sqrt{(0-(-a-b))^2+(0-c)^2}$

$\implies |DG|=\sqrt{a^2+b^2+c^2+2ab}$

$|GF|=\sqrt{((a+b)-0)^2+(c-0)^2}$

$\implies |GF|=\sqrt{a^2+b^2+c^2+2ab}$

$|EF|=\sqrt{((a+b)-0)^2+(c-2c)^2}$

$\implies |EF|=\sqrt{a^2+b^2+c^2+2ab}$

$|DE|=\sqrt{(0-(-a-b))^2+(2c-c)^2}$

$\implies |DE|=\sqrt{a^2+b^2+c^2+2ab}$

Using the slope formula; $m=\frac{y_2-y_1}{x_2-x_1}$

The slope of EG is $m_{EG}=\frac{2c-0}{0-0}$

$\implies m_{EG}=\frac{2c}{0}$

The slope of EG is undefined hence it is a vertical line.

The slope of DF is $m_{DF}=\frac{c-c}{a+b-(-a-b)}$

$\implies m_{DF}=\frac{0}{2a+2b)}=0$

The slope of DF is zero, hence it is a horizontal line.

A horizontal line meets a vertical line at 90 degrees.

Conclusion:

Since $|DG|\cong |GF| \cong |EF| \cong |DE|$ and $DF \perp FG$ , DEFG is a rhombus

b) Using the slope formula:

The slope of DE is $m_{DE}=\frac{2c-c}{0-(-a-b)}$

$m_{DE}=\frac{c}{a+b)}$

The slope of FG is $m_{FG}=\frac{c-0}{a+b-0}$

$\implies m_{FG}=\frac{c}{a+b}$

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3 years ago

Jamie has $12.63 and Jill has $4.58. What is the total amount of money, in

Usimov [2.4K]

Answer:

$17.21

Step-by-step explanation:

Just line up the decimals and then you add. But after you finished adding, make sure you just straight up bring the decimal down to your final answer to the question.

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3 years ago

The total number of living humans on Earth was converted to scientific notation using an online calculator and was reported to b

MakcuM [25]

The answer is in the questio

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3 years ago

to recover a large chair in your home, you purchase 9 1/2 yards of upholstery fabric at $11.00 per yard. If there is 7% sales ta

KATRIN_1 [288]

11.00*9.5=104.5
104.5*0.07=7.315
7.315+104.5=111.815

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3 years ago

Solve for x:<br> 2/3+1/3x=2x

igomit [66]

2/3+1/3x=2x
2+1x=6x
x-6x=-2
-5x=-2
x=2/5

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3 years ago