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podryga [215]
3 years ago
15

b is the midpoint of AC and E is the midpoint of BD if A(-9,-4) C(-1,6) and E(-4,-3) find the coirdinates of D

Mathematics
1 answer:
natima [27]3 years ago
5 0

To find the coordinate of the point D, we can use the Midpoint point of a line Segment formula. Calculation of the formula are as follows,

Given two points A(x1,y1) and C(x2,y2), we need to locate the midpoint coordinate of this line denoted as B(x,y).

To solve for the value of x and y, we get,

x=(x1+x2)/2 and y=(y1+y2)/2

For the given problem, we need to solve first the midpoint coordinate of AC which is B.

So, A(-9,-4)=A(x1,y1) and C(-1,6)=C(x2,y2)

Hence,

B(x,y)=B((-9+(-1))/2, (-4+6)/2)=B(-10/2,2/2)=B(-5,1)

Now, since the midpoint is given but one point in the line is missing. To solve for the missing point D(x2,y2), we need to use the Midpoint Segment Formula.

 That is, B(-5,1)=B(x,y) and E(-4,-3)=E(x1,y1)

So,

x=(x1+x2)/2 and y=(y1+y2)/2

-5=(-4+x2)/2 and 1=(-3+y2)/2

By Cross Multiplication and Transposing method,

-5(2)=-4+x2 and 1(2)=-3+y2

x2=-10+4=-6 and y2=3+2=5

Thus, the coordinate of D is D(-6,5).

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Proportional relationship???
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Answer:

Step-by-step explanation:

Yes this is Proportional

3 0
3 years ago
HURRY ILL GIVE U BRAINLIEST!!! Find the area of each figure. Which do these belong in?
nordsb [41]

Answer:

Area of rectangle PQRS is 14 square units.

Area of triangles UVW and EFG and square ABCD are 16 square units each.

Step-by-step explanation:

Let us find the area of each of the figures shown in the graph.

Area of rectangle PQRS is given as the product of PQ and QS.

From the graph,

Length of PQ = 7 units

Length of QS = 2 units

Now, area of rectangle PQRS = PQ\times QS=7\times 2=14 square units.

Now, area of square ABCD is given as the square of any of its side.

From the graph, AB = 4 units.

So, area of ABCD = AB^{2}=4^2=16 square units.

Area of triangle UVW is given as the half of the product of its base VW and height UW.

From the graph, UW = 4 units, VW = 8 units

Therefore, area of triangle UVW = \frac{1}{2}\times UW\times VW=\frac{1}{2}\times 4\times 8=16 square units.

For triangle EFG, EF = 4 units and FG = 8 units.

Area =  \frac{1}{2}\times EF\times FG=\frac{1}{2}\times 4\times 8=16 square units.

Area of rectangle PQRS is 14 square units. The remaining figures have areas each equal to 16 square units.

4 0
3 years ago
In country​ A, the number of highway bridges for the years 2000 to 2005 can be modeled by the equation y=149(x+1.5)^2+489,505, w
EleoNora [17]
Given that the number of bridges has been modeled by the function:
<span>y=149(x+1.5)^2+489,505
To find the year in which, y=505000 we shall proceed as follows:
From:
</span>y=149(x+1.5)^2+489,505
substituting y=505000 we shall have:
505000=149(x+1.5)^2+489,505
simplifying the above we get:
0=149(x+1.5)^2-15495
expanding the above we get:
0=149x^2+447x+335.25-15495
simplifying
0=149x^2+447x-15159.8
solving the quadratic equation by quadratic formula we get:
x~8.69771 or x~-11.6977
hence we take positve number:
x~8.69771~8.7 years~9 years
thus the year in which the number will be 505000 will be:
2000+9=2009
4 0
3 years ago
Liam buys a motorcycle for $2,900. Its value depreciates annually at a rate of 12%. At the end of t years, it has a value of les
KIM [24]

It is given in the problem that

Liam buys a motorcycle for $2,900

Its value depreciates annually at a rate of 12%=0.12

At the end of t years, it has a value of less than $2,000

The exponential equation modeling this situation can be written as below

2900(1-0.12)^t

The inequality representing its value less than $2,000 can be written as below

2900(1-0.12)^t

4 0
3 years ago
What is the difference in length between the longest meteor and the shortest meteor?
hichkok12 [17]
1 5/8
1 7/8 - 2/8= 8+7/8 - 2/8= 15/8 - 2/8= 13/8=
1 5/8 is the answer
6 0
3 years ago
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