The coordinates of the endpoints of and are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which condition proves that ?Please Look A Picture For A Better Look At The Question.

Answers

Answer 1

Answer: for two line segments to be parallel, their slopes must be equal.

Therefore slope of AB must be equal to slope of CD

which is, option 3
(y4-y3)/(x4-x3)=(y2-y1)/(x2-x1)

Answer 2

Answer:

Answer with explanation:

When two lines are parallel, then their slopes are equal.

It is given that, AB ║ CD.

Coordinates of A, B, C and D are,

$A(x_(1), y_(1)), B(x_(2), y_(2)), C(x_(3), y_(3)), and D(x_(4), y_(4))$

→→Slope of AB=Slope of CD

$\rightarrow(y_(2)-y_(1))/(x_(2)-x_(1))=(y_(4)-y_(3))/(x_(4)-x_(3))$

Option : C

Related Questions

You have a long-distance calling card with a remaining balance of $12.00. It costs $4.25 for the first 5 minutes and then an additional $0.40 for each additional minute. How many minutes do you have remaining on the card? Round your answer to the nearest whole number. A. 10 B. 16 C. 22 D. 17 E. 24
A musical instrument depreciates by 20% of itsvalue each year. What is the value, after 2 years, of a piano purchased new for $1200?
What's the length of one leg of a right triangle if the length of the hypotenuse is 25 units and the length of the other leg is 15 units? A. 10 units B. 20 units C. 24.7 units D. 29.2 units
Which pair is a base and corresponding height for the triangle?A. b = 16 units and h = 9.6 unitsB. b = 20 units and h = 16 unitsC. b = 20 units and h = 9.6 unitsD. b = 20 units and h = 12 units
Does anyone do pltw?

The sum of a number and twice the second number is 24. Determine the two numbers to maximize their product. Show your work (equations, calculations, etc.) If it is easier to describe in detail what you did rather than show something (such as using your calculator), you may do so.

Answers

The sum of a number and the second number is 24.
$a+2b=24$

We want to find the maximum product of $ab$ .

Let's solve our first equation for a.
$a=24-2b$

We can substitute this in $p=ab$ so that we only have one variable.
$ab=(24-2b)b$

Distribute.
$p=-2b^2+24b$

Now we can just find the vertex of this quadratic, either putting it or vertex form or using a shortcut mentioned later. (if your teacher has already explained it to you)

Put the constant on the left side. (It's 0, so nothing to do there)

Factor out the coefficient of b².
$p=-2(b^2-12b)$

Find which number to add to create a perfect square trinomial.
(half of -12 is -6, -6² = 36. we would add -72 to each side, so that 36 ends up inside the parentheses on the right side)
$p-72=-2(b^2-12b+36)$

Factor the perfect square trinomial.
$p-72=-2(b-6)^2$

Isolate the p term.
$72=-2(b-6)^2+72$

The vertex is (6, 72), as vertex form is y=a(x-h)²+k where (h, k) is the vertex.
Therefore, the value of b which yields the height product p is 6.
We can plug this into a previous equation to find a.
a + 2b = 24
a + 2(6) = 24
a + 12 = 24
a = 12

a = 12, b = 6

(The shortcut I was talking about is that for any quadratic f(x) = ax² + bx + c, the vertex (h, k) is (-b/2a, f(h)))

Answer:

The total length of Valerie’s walls is 105.75 feet:

(2.5 × 4) + (21.25 × 3) + 32 = 10 + 63.75 + 32 = 105.75 feet.

The total length of Seth’s walls is 107 feet:

3.5 + (22.75 × 2) + 58 = 3.5 + 45.5 + 58 = 107 feet.

The sum of 105.75 feet and 107 feet is 212.75 feet. The Commutative Property allows me to add numbers in any order. This is why the answers in parts D and E match.

Step-by-step explanation:

If your on PLATO this is the answer

Divide £50.00 in the ratio of 1:4 SOMEBODY HELP!!!!

Answers

1+4=5
50.00/5=10
1 unit is 10
1 unit to 4 unit

10 times 1=10
10 times 4=40

1:4
10:40

Which set of sides will make a triangle?10cm, 5cm, 9cm
10cm, 3cm, 4cm
1cm, 3cm, 1cm
5cm, 2cm, 3cm

Answers

Answer:

10cm 5cm and 9cm

Step-by-step explanation:

just try this

take any two measurements and add them together if they are larger than the 3rd measurement it will work and all you have to do is do that to each measurement

10+5 is greater than 9

9+5 is greater than 10

9+10 is greater than 5

Between what two consecutive integers does√73
lie????

A: 71 and 73
B: 8 and 9
C: 9 and 10
D: 10 and 11

Answers

Hey there, √73 is between the two square roots, √81 and √64, now, 8*9=72, so, √64, √73, and √81. So, 8<√73<9. Therefore, the answer is B. 8 and 9

What is the equation for a geometric sentence?(4, 12, 36, 108...)
(36, 18, 9, 9/2...)
(-2, 20, -200, 2000...)

Answers

1) 12/4 =3
2) 18/36 = 1/2
3) 20/-2 =-10

How to find the perimeter and the area of a rectangle on a coordinate plane using the distance formula? : A(3,8) B(5,4) C(-4,-1) D(-6,3) Round to the nearest tenth if necessary.

Answers

I used some site to plot the points.

First, let's recall the formulas for Perimeter and Area of a Rectangle.
Perimeter = 2(l+w)
Area = l×w
Also, the distance formula is
D = $\sqrt{( x_(2)-x_(1))^2+{(y_(2)-y_(1))^2}$

Now, we need to determine l and w.
So, the length is the distance of AD or BC
and the width is the distance of DC or AB
(I'll just use the sides that I've labelled for ease)

So first to determine the length, we need to calculate the distance of AD
Points are A(3,8) and D(-6,3)
$x_(1) =3, x_(2) =8, y_(1) =6, y_(2) =-3$
$D_(AD)= \sqrt{( 6-3)^2+{(-3-8)^2}$
$D_(AD)= √((3)^2+(-11)^2)$
$D_(AD)= √(9+121)$
$D_(AD)= √(130) ≈ 11.40$
So the length of the rectangle is 11.40 units.

Now, the width!
So first to determine the width, we need to calculate the distance of DC
Points are D(-6,3) and C(-4,-1)
$x_(1) =6, x_(2) =-4, y_(1) =-3, y_(2) =-1$
$D_(DC)= \sqrt{(-4-6)^2+{(-1- -3)^2}$
$<span>D_(DC)= \sqrt{(-4-6)^2+{(-1+3)^2}$
$D_(DC)= √((-10)^2+(2)^2)$
$D_(AD)= √(100+4)$
$D_(AD)= √(104) ≈ 10.20$
So the width of the rectangle is ≈10.20 units.

Let's now solve for Perimeter and Area using
l = 11.40
w = 10.20

Perimeter = 2(l+w)
Perimter = 2(11.40+10.20)
Perimter = 2(21.60)
Perimter = 43.2 units

Area = l×w
Area = (11.40)(10.20)
Area = 116.28
Area = 116.3 units² (rounding)

In conclusion, given points A(3,8) B(5,4) C(-4,-1) D(-6,3), the Perimeter is 43.2 units and the Area is ≈116.3 units² using the distance formula.

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