The endpoints of a side of rectangle ABCD in the coordinate plane are at A (2, 11) and B (7, 1). Find the equation of the line t
hat contains the given segment. The line segment is AD. The equation is y = .
2 answers:
Answer:
Step-by-step explanation:
Given that ABCD is a rectangle. A is (2,11) and B (7,1)
To find equation of AD
AD is perpendicular to AB and passes through A
To find slope of AB
Slope = change in y/change in x =
Slope of AB = slope of perpendicular line =
Using point slope formula we get equation of AD is
We know that
<span>A (2, 11) and B (7, 1)
step 1
find the slope of a line AB
the slope m=(y2-y1)/(x2-x1)------> m=</span>(1-11)/(7-2)---> m=-10/5----> m=-2
step 2
find the equation of a line AD
we know that
the segment AB and the segment AD are perpendicular
so
m1*m2=-1
m2=-1/m1-----> m2=1/2
with the slope m2=1/2 and the point A(2,11)
y-y1=m*(x-x1)------> y-11=(1/2)*(x-2)----> y=(1/2)x-1+11
y=(1/2)x+10----> y=0.5x+10
the answer is
the equation of a line AD is y=0.5x+10
see the attached figure
<span>A (2, 11) and B (7, 1)
step 1
find the slope of a line AB
the slope m=(y2-y1)/(x2-x1)------> m=</span>(1-11)/(7-2)---> m=-10/5----> m=-2
step 2
find the equation of a line AD
we know that
the segment AB and the segment AD are perpendicular
so
m1*m2=-1
m2=-1/m1-----> m2=1/2
with the slope m2=1/2 and the point A(2,11)
y-y1=m*(x-x1)------> y-11=(1/2)*(x-2)----> y=(1/2)x-1+11
y=(1/2)x+10----> y=0.5x+10
the answer is
the equation of a line AD is y=0.5x+10
see the attached figure
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Money received in tenth month: $104
Difference between explicit formula and a recursive formula is: the use of (n-1)th term, nth term and the common difference (d) brings a great difference between the two formulae of an arithmetic progression.
<h3>What is arithmetic progression?</h3>A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
- Money received in first four months: $50, $52, $55, %59.
To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: , n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
(b) Difference between explicit formula and recursive formula of an arithmetic progression:
- The first term of a recursive formula is a₁ and the formula for the nth term uses the first term and the common difference, d. One example of a recursive formula is
.
- A formula for the nth term in an explicit formula would include the initial term a₁, the common difference d, and the term number, n. The equation
.
To learn more about arithmetic Progressions, refer to the link: brainly.com/question/6561461
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