M is the midpoint of AN, A has coordinates
(-7,4), and M has coordinates (-4, -1). Find
the coordinates of N.
Help explain pls?
Answers
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Explanation:
Let's focus on the x coordinates of each point for now.
Point A has x coordinate -7Point N has an unknown x coordinate. We leave it as x for now.Point M has x coordinate -4The idea to find the midpoint's coordinates is to add up the endpoints coordinates and divide by 2.
So we'll add up -7 and x, then divide by 2 to get the midpoint x coordinate of -4
In short we have: (-7+x)/2 = -4
Solving for x leads to...
(-7+x)/2 = -4
-7+x = 2*(-4)
-7+x = -8
x = -8+7
x = -1
This is the x coordinate of point N
-------------------------------
We'll repeat the same idea and steps for the y coordinates
Point A has y coordinate 4Point N has y coordinate unknown. Leave it as y for now.Point M has y coordinate -1So,
(4+y)/2 = -1
4+y = 2(-1)
4+y = -2
y = -2-4
y = -6
This is the y coordinate of point N.
------------------------------
In summary, we found that point N is located at (-1, -6)
Point A is (-7,4) and point N is (-1,-6)
If you apply the midpoint formula to those two points, you should find the midpoint to be M(-4,-1) which helps confirm the answer.
Another way to confirm the answer is to compute the distance from A to M, which finds the length of segment AM. Do the same for segment MN. You should find that both segments are the same length.
The diagram below is a visual way to check. Starting at point A and moving down to point B, we moved 5 units. Then go from B to M and you'll move 3 units to the right. This pattern "down 5, right 3" is applied again when we go from M to C to N in that order. This effectively creates two congruent triangles (ABM and MCN) which can lead to proving AM = MN.
In short: the red piece of the graph is the same length as the blue piece; this confirms we have the correct answer.
Step-by-step explanation:
According to Question , M is the midpoint of AN, A has coordinates (-7,4), and M has coordinates (-4, -1).
Figure :-
[tex] \setlength{\unitlength}{1 cm}\begin{picture}(20,12) \put(4,0.2){\line(0,-1){0.4}}\put(1,0){\line(1,0){6}} \put(3.8,-0.6){$\bf M(-4,-1) $} \put(1,-0.6){$\bf A (-7,4)$} \put(6.8,-0.6){$\bf N(x,y)$} \end{picture}[/tex]
Let the coordinates of N be ( x , y )
Now , according to Midpoint Formula , the midpoint of points say A(x , y) and B (x' , y') is given by ,
[tex]\boxed{\blue{ \bf Midpoint =\bigg( \dfrac{x+x'}{2} , \dfrac{y+y'}{2} \bigg) }}[/tex]
On using this formula ,
[tex]=> Midpoint = \bigg( \dfrac{x+x'}{2} , \dfrac{y+y'}{2} \bigg) \\ \\ => (-4, 1) = \bigg( \dfrac{x -7 }{2} , \dfrac{y + 4 }{2}\bigg) \\ \\ => -4 = \dfrac{x-7}{2} \\\\ => x - 7 = -8 \\\\ => x = 7 -8 \\\\ \boxed{\red{\sf=> x = -1 }} \\\\ => \dfrac{y+4}{2}=-1 \\\\=> y +4 = -2 \\ \\ y = -4-2 \\\\\boxed{\red{\sf=> y = -6 }}[/tex]
Related Questions
What is the average rate of change of f(x) = 5x – 7 from x = -3 to x = 7?
Answers
Answer:
[tex]f(x) = 5x - 7 \\ change = f(7) - f( - 3) \\ = ((5)(7) - 7) - ((5)( - 3) - 7) \\ = (35 - 7) - ( - 15 - 7) \\ = (28) - ( - 22) \\ = 50 \\ average \: change = \frac{change}{2} \\ = \frac{50}{2} \\ = 25[/tex]
The rate of change of function f(x) = 5x - 7 from x = -3 to x = 7 will be equal to 5.
A function f(x) = 5x - 7 is given which changes from x = -3 to x = 7.
We have to find out the average rate of change for the given function.
What is the average rate of change of function from [tex]x_{1}[/tex] to [tex]x_{2}[/tex] ?
The average rate of change of function from [tex]x_{1}[/tex] to [tex]x_{2}[/tex] can be given by a formula which is [tex]\frac{f(x_{1})-f(x_{2})}{x_{1} - x_{2}}[/tex].
As per the question ;
The function is f(x) = 5x - 7
So,
At x = -3
f(x) = 5 × -3 - 7
f(x) = -15 - 7
f(x) = -22
At x = 7
f(x) = 5 × 7 - 7
f(x) = 35 - 7
f(x) = 28
Let's use the formula to find average rate of change of function ;
i.e.,
= [tex]\frac{f(x_{1})-f(x_{2})}{x_{1} - x_{2}}[/tex]
= [tex]\frac{(28)-(-22)}{7-(-3)}[/tex]
= [tex]\frac{28+22}{7+3}[/tex]
= [tex]\frac{50}{10}[/tex]
= 5
Thus , the rate of change of function f(x) = 5x - 7 from x = -3 to x = 7 will be equal to 5.
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Find the value of x
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Answers
Answer:
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11x-1+20x-3=151 (the exterior angle of an triangle is equal to the sum of two opposite interior angles)
31x-4=151
31x=151+4
31x=155
x=155/31
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14x-13=4x+13+6x+2
14x-4x-6x=13+13+2
4x=28
x=28÷4
x=7°
Determine which of the following terms are not considered to be like terms with the expression -6s2t. Select all situations that apply.
( s2)( t)
10 ∙ s2 ∙ t
4( s ∙ t)
-6( s2 + t)
s2t
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Answers
Answer:
[tex](s^{2})(t) , 10^{2}t, s^{2}t[/tex] are the correct answers
Step-by-step explanation:
The others don't work because they don't have the same power for each variable.
Answer:
It is s^2(t), 10 *s^2 * t, and (1/4) (s^2)(t)
What is the slope of the line through (0,-1) and (2,3)?
Answers
(3+1)/(2-0) = 4/2 = 2
The slope is 2
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Answers
Answer:
2
Step-by-step explanation:
Answer:
B: 9
Step-by-step explanation:
1/4(c^3 + d^2)
Plug in -4 for C and 10 for d
1/4((-4)^3 + (10)^2)
(-4)^3 = -64
10^2 = 100
1/4(-64 + 100)
-64 + 100 = 36
1/4(36)
= 36/4 = 9
9 is the final answer.
In a survey four out of seven people named blue as their favorite color. One out of three
named red IF 1,092 people were included in the survey, how many named neither blue nor red
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Step-by-step explanation:
The answer is on the picture.
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Answer:
x = -70
Step-by-step explanation:
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Answer:
The answer is 1/2
Step-by-step explanation:
1/3 x 3/2
To break it up you multiply the top numbers to get 3
The you'd multiply the bottom numbers to get 6
so your answer is 3/6 which is also equal to 1/2
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Answers
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0.205 (rounded)
Step-by-step explanation:
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Answer:
it is b my guy :)
Step-by-step explanation:
Pam read 126 pages of her summer reading bookin 3 hours. Zac read a180 pages of his summer reading book in 4 hours. If they continue to read at the same speeds, will they both finish the 215 page book after 5 total hours of reading?
Answers
Answer:
Zac will finish, Pam won’t
Step-by-step explanation:
Let’s have the individual reading speeds
The individual reading speeds are the number of pages divided by hours taken
For Pam; 126/3 = 42 pages per hour
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Answers
Answer:
aby/2 = c
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Answers
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Step-by-step explanation:
Answer:
d
Step-by-step explanation:
A farmer is selling apples from his orchard. He uses the equation c = 1.6pto calculate the total cost, c, for every pound of apples, p.
a.) How much does a customer pay for 1 pound of apples?
b.) How much would 8.5 pounds of apples cost?
c.) A customer spent $5.20. How many pounds of apples did they purchase?
Answers
Answer:
A) $1.60
B) $13.60
C) 3 1/4 lb
Step-by-step explanation:
What we know:
A farmer uses the equation c = 1.6p to calculate the total cost, c, for p pounds of apples.
A) 1 pound would cost $1.60, as that is the unit rate.
B) 8.5 * 1.6
8.5 + (0.6 * 8.5)
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C) 5.2/1.6
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Answers
Answer:
y = 5x - 5Step-by-step explanation:
slope-intercept form of equation: y = mx + b
where m is slope and b is y-intercept
If line y=ax+b passes through point (x₀,y₀) that means
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y = 5x - 5.
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Answers
Answer:
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Answers
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Answers
Answer:
45z-40z=5+90
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Answers
Answer:
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How many comic books does Diego have if Han has:
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Answers
Answer:
Han has 9 books
Step-by-step explanation:
If diego has 27 comic books than that means that all you have to do is divide 27/3. then that equals to 9
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Answers
Answer:
I got 28
Step-by-step explanation:
I use the slope formula
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{224-140}{8-5} =\frac{84}{3} =28[/tex]
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A. They are the same size and shape.
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D. They have corresponding sides that are congruent.
Answers
Answer:
A
Step-by-step explanation:
Ortiz used similar triangles to make a design. Which statement about the triangles in the design must be true? They are the same size and shape.
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B.3
C.2
D.4
Answers
Have a great day! Hope that is the answer.
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Answer:
last one is correct
Step-by-step explanation:
Step-by-step explanation:
is the last one
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Answers
Using the common denominator, what is an equivalent fraction to 11/8 ?
Answers
Answer:
Equivalent fractions to 11/8
11/8, 22/16, 33/24, 44/32, 55/40, 66/48, 77/56, 88/64, 99/72, 110/80
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name:
a chord
a diameter
a radius
a minor arc
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Answers
Ab diameter
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Jada has a meal in a restaurant. She adds up the prices listed on the menu for everything they ordered and gets a subtotal of $42.00.
c) They actually pay $52.99. The additional $7 is a tip for the server. What percentage of the subtotal is the tip?
Answers
Answer: See explanation
Step-by-step explanation:
Your question wasn't well written but I saw an identical question so let me help out.
a. Jada has a meal in a restaurant she adds up the prices listed on the menu for everything they ordered and gets a subtotal of $42.00. When the check comes, it says they also need to pay $3.99 in sales tax. what percentage of the subtotal is the sales tax?
b. They actually pay $52.99. The additional $7 is a tip for the server. What percentage of the subtotal is the tip?
a. Subtotal = $42.00
Tax = $3.99
Percentage of subtotal that is sales tax will be:
= Sales tax/Subtotal × 100
= 3.99/42.00 × 100
= 9.5%
b. Tip = $7
Sub total = $42
The percentage of the subtotal that is the tip will be:
= Tip/Sub total × 100
= 7/42 × 100
= 16.67%