Quadrilateral ABCD is graphed on a coordinate plane. Three of its vertices are at A(2,6), Point B(6,8), and Point C(8,4). Which of the following additional statements is sufficient to prove that quadrilateral ABCD is a square
Answers
Answer:A
Step-by-step explanation:
Got it right in my test lolz
You can use the fact that diagonal of a square are equal and perpendicular to each other.
The option D: Segment BD has a slope of 3 and a length of [tex]2\sqrt{10}[/tex]
Given that:A has coordinate (2,6)B has coordinate (6,8)C has coordinate (8,4)When is ABCD square?One theorem in mathematics states that:
"If diagonals of a quadrilateral are equal and perpendicular to each other, then that quadrilateral is a square."
Using the fact that diagonal of a square are equal and perpendicular to each other:For ABCD to be square, we need AC and BD to be of equal length and perpendicular to each other.
Two lines are perpendicular if their slopes are negative reciprocal of each other.
Slope of AC:[tex]Slope(AC) = \dfrac{rise}{run} = \dfrac{C_y - A_y}{C_x - A_x} = \dfrac{4-6}{8-2} = -\dfrac{1}{3}[/tex]
Thus, slope of BD needed to be negative reciprocal of -1/3 which is 3 for ABCD to be square (first needed condition)
Length of AC:[tex]|AC| = \sqrt{(C_y - A_y)^2 + (C_x - A_x)^2} = \sqrt{(4-8)^2 + (8-6)^2} = \sqrt{2^2 + 6^2} = \sqrt{40} = 2\sqrt{10}[/tex]
The second condition needs |BD| = |AC|.
Thus, length of BC should be [tex]2\sqrt{10}[/tex]
Thus, the sufficient condition for ABCD to be a square is:
Option D: Segment BD has a slope of 3 and a length of [tex]2\sqrt{10}[/tex]
Learn more about square and its diagonals here:
https://brainly.com/question/3417399
Related Questions
Josette found 16 coins in her purse. She had 2 more nickels than pennies and 7 fewer quarters than pennies. Josette modeled the scenario in a table and then wrote the equation p + (p + 2) + (7 – p) = 16.
A 2-column table with 3 rows. Column 1 has entries pennies, nickels, quarters. Column 2 has entries p, p + 2, blank.
Is Josette’s equation correct? If not, what was her mistake.
Answers
Answer:
The number of quarters was translated incorrectly and should be p – 7.
Answer:
D. The number of quarters was translated incorrectly and should be p – 7.
I'm taking the assignment and I got it right just now
Step-by-step explanation:
100 bushels of corn are divided among 100 people: men, women, and children. Men get 3 bushels each. Women get 2 each. Children get 1/2 bushel each. How can the bushels be distributed?
Answers
Answer:
Step-by-step explanation:
100 bushels of corn are divided among 100 people: men, women, and children. Men get 3 bushels each. Women get 2 each. Children get 1/2 bushel each. How can the bushels be distributed?
Please someone help!!!!
Answers
Tell me if u need more help :)
Suppose Marcy's rectangular laptop measures 12 inches by 9 inches. Find the area of her
laptop and express your answer to the nearest square centimeter.
[Ar= L•W]
L=length W=width A=area Ar=? 1inch=2.54 centimeters
A 696 square centimeters
B 697 square centimeters
C 660 square centimeters
D 658 square centimeters
Answers
Answer:
B
Step-by-step explanation:
Sana makatulong answer ko
697 square centimeters
Step-by-step explanation:
<3
The regular price is $24.50. Your discount is15% off. What is the sale price of your shirt?
Someone pls help me
Answers
Answer:
$3.68
Step-by-step explanation:
What is the slope of the line through (-5,-10) and(-1, 5)?
Answers
Answer: The slope is 15/4.
Step-by-step explanation:
M = (y2 - y1)/(x2 - x1)
M = (5 - (-10))/(-1 - (-5))
M = (5 + 10)/(-1 + 5)
M = 15/4
(I BEG U TUTORS HALP) the linear equation. Y= -1/3 x+5 is shown graphed. If it was combined with the equation y=5/3 x-3 to form a system what would be the solution to this system? Show how you arrived at your answer
Answers
Answer: the solution of the sytem is x = 4, y = 11/3.
Step-by-step explanation:
There are multiple ways to solve this, you could just graph the other line and see at which point both lines intersect, that point is the solution of the system.
I will do it in a more analytical way.
We have the two equations:
y = -(1/3)*x + 5
y = (5/3)*x - 3
x and y represent the same number.
then we must have y = y
then we can write:
-(1/3)*x + 5 = y = (5/3)*x - 3
this means that:
-(1/3)*x + 5 = (5/3)*x - 3
Now we can solve this for x.
To do it, let's move all the terms with x to the left, and the terms without x to the right:
-(1/3)*x - (5/3)*x = -3 - 5
-(6/3)*x = -8
-2*x = -8
x = -8/-2 = 4
We found the value of x, now we can replace this in one of the two equations to get the value of y.
Let's use the first equation:
y = -(1/3)*4 + 5 = -4/3 + 5 = -4/3 + 15/3 = (15 - 4)/3 = 11/3
Then the solution of the sytem is x = 4, y = 11/3.
Also can be written as (4, 11/3).
She wants to use one-third of her bead collection to make bracelets for 5 friends. What fraction of her collection should she use for each bracelet?
Answers
Answer: 1/15
Step-by-step explanation:
The lady wants to use 1/3 of her bead collection to make 5 bracelets for 5 friends.
This means that the amount of beads required for each bracelet is be 1/3 divided by the 5 bracelets:
= 1/3 ÷ 5
= 1/3 * 1/5
= 1/15 of her collection
When dividing fractions, you can instead multiply the inverse of the second fraction to get your answer.
Hello can some one answer all these
752 divided 47
375 divided by 25
576 divided by 24
(5 points)
Answers
2. 15
3. 24 hope this helps!
Answer:
1. 752/47=16
2. 375/25=15
3. 576/24=24
hope this helps!!:)
Step-by-step explanation:
1.
1. Find the Greatest Common Factor (GCF) of 752 which is 47 .
2. Divide both the numerator and the denominator by the GCF.
752/47
47/47
3. simplify
16
hope this helps!!:)
The midsegment of a trapezoid is a segment whose _____ are the midpoints of the legs of a trapezoid.
Answers
Answer:Joints
Step-by-step explanation:
It is likely the joining point so it is so help ful
there are two similar toys
Answers
The real solution for x2 = 25
Answers
Answer:
x = 12.5 or 12 1/2 (depends if you want decimal or fractions)
Step-by-step explanation:
Find the measure of each numbered angle
Answers
Answer:
m<1 = 40°
m<2 = 118°
m<3 = 71°
Step-by-step explanation:
✔️m<2 = 180° - 62° (angles in a straight line/supplementary angles)
m<2 = 118°
✔️m<1 = 180° - (118° + 22°) (sum of ∆)
m<1 = 40°
✔️m<3 = 180 - (47 + 62) (sum of ∆)
m<3 = 71°
On their field trip to the circus, the 30 students in Ms. Dalton's class plan to buy 15 bags of peanuts to share. Each bag contains 0.9kg of peanuts. How much is needed to fill 15 bags?
Answer: kg of peanuts
Answers
Answer:
13.5 kg of peanuts are needed to fill 15 bags.
Please mark as brainliest
Step-by-step explanation:
Let a equal the total kg of peanuts.
[tex]a=0.9(15)\\a=13.5\\[/tex]
Simplify each expression and evaluate it for x=3 13 . 3(2x+6)−(3x+1) The simplified expression is : The value of the expression for the given x is :
Answers
Answer:
Simplified expression; 3x + 17
The value of the function for the given value of x is 26
Step-by-step explanation:
Restructured
Simplify each expression and evaluate it for x=3, 3(2x+6)−(3x+1) The simplified expression is : The value of the expression for the given x is :
Given the expression;
3(2x+6) - (3x-1)
On simplification:
= 3(2x) + 3(6) -3x + 1
= 6x + 18 - 3x + 1
= 6x - 3x + 18-1
= 3x + 17
If x = 3
f(3) = 3(3) + 17
f(3) = 9 + 17
f(3) = 26
Note the question was re-structured since the given question was not too clear
Write two numbers that multiply to the value on top and add to the value on bottom?
Answers
5 x 2 = 10
5 + 2 = 7
An employee puts 10000 in a retirement account that offers 4% interest. How much will he have in 12 years
Answers
Answer:
14800
Step-by-step explanation:
The formula for simple interest (I) in terms of principal (P), rate (R) and time (T) is given as follows;
I = P x R x T / 100 ------------- (i)
Given:
Principal (P) = Initial amount being put into the account = 10000
Rate (R) = The interest rate being offered by the account manager = 4%
Time (T) = Time taken = 12 years
Substitute these values into equation (i) as follows:
I = 10000 x 4 x 12 / 100
I = 4800
Therefore, the initial amount will yield an interest of 4800 for those 12 years.
The total amount the employee will thus have in 12 years will be the sum of the initial amount and the interest. i.e
Amount = P + I
Amount = 10000 + 4800
Amount = 14800
There are ten people in the Baking Club, including Mark. They choose $3$ people to form an executive committee. How many possible committees could be formed that include Mark?
Answers
Answer:
120 ways
Step-by-step explanation:
We have the total number of people in this baking club = 10, Mike inclusive.
We are asked to find how to form an executive committee of 3 from these 10 people
We solve this using combination method
10C3
= 120 possible committees
So out of these 10 people we can select a committee of 3 persons in 120 ways.
Thank you.
I’ll give Brainliest.
Show steps as well please
Point D is the in center of triangle ABC. Write an expression for the length x in terms of the three side lengths AB, AC, BC.
Hint: Use areas of triangles...A=1/2bh
Answers
Answer:
[tex]x = \frac{2(A_T) }{(AB) + (AC) + (BC)} [/tex]
Please help!!!! 20 points!!!!
Answers
Answer:
Please show what the drop bars show
Step-by-step explanation:
That way we know the options <3
If f(x) = 5x+4 and g(x) = x-4, find (f o g)(x) and (g o f)(x)
Answers
Step-by-step explanation:
F(g(x)) = F(x-4)
= 5(x-4) +4
= 5x-20+4
=5x-16
G(f(x)) = G(5x-4)
= (5x-4) -4
= 5x-8
Drake and Josh are brothers. Their ages add to 29. Drake is 4 years younger than twice Josh's age. How old are they?
Answers
Answer:
Drake: 18
Josh: 11
Step-by-step explanation:
11*2=22
22-4 = 18
11+18= 29
numerical coefficients of (I need dis quick would appreciate it)
Answers
Answer:
xy(5-6xy)/4
Step-by-step explanation:
Here, we want to evaluate the expression given
We have this as ;
(5xy - 6x^2y^2)/4
= xy(5-6xy)/4
Also Urgent!!!
Click on the photo <3
Answers
Answer:
1st option is correct
Step-by-step explanation:
because power gets add up when base is same in inti
Find the exact length of the third side.
78
30
Answers
the volume of two sphere are the ratio 125:64 find the ratio of there radii plz now
Answers
Answer:
3.1 : 2.48
Step-by-step explanation:
The volume of two sphere are the ratio 125:64
The volume of a sphere = 4/3 × π × r³
Hence, we have to find the radius of the cylinder
The formula for radius of the cylinder =
(3V/4π)⅓
For sphere 1
Volume = 125
=( 3 × 125/4 × π)⅓
= 3.1
For sphere 1
Volume = 64
=( 3 × 64/4 × π)⅓
= 2.48
The ratio of their radii =
3.1 : 2.48
Which property is being used?
Answers
Answer:
Associative Property.
Plz help I’m confused^
Answers
Answer:
a) missing exponent is 8
b) missing exponent is -5
c) missing exponent is 15
d) missing exponent is 6
Step-by-step explanation:
for 'a' and 'b' you have to ADD the exponents
for 'c' you have to SUBTRACT the exponents
for 'd' you have to MULT the exponents
let 'n' = missing exponent
a) -5 + n = 3
n = 8
b) 3 + n = -2
n = -5
c) n - 6 = 9
n = 15
d) 5n = 30
n = 6
if a play station was purchased for $558 after 10% discornt what was the origanal price of the play station
Answers
Answer:
nxejcxjwxjw kjxn
Step-by-step explanation:
nxke jxin jinjid c i
there are 23 students in a class. 17 of the students are female. find the percentage of the class that are female. give your answer to the nearest percent.
