Answer:
The coordinates of P is (-1,5.5)
Step-by-step explanation:
Here, we want to find the coordinates of the point that divides the segment into the ratio 1 to 3
To do this, we are going to use the section formula
We have this as;
(x,y) = (nx1 + mx2)/m+ n, (ny1 + my2)/m + n
where m = 1 , n = 3
(x1,y1) = (-3,4)
(x2,y2) = (5,10)
Substituting these values, we have;
(x,y) = (3(-3) + 1(5)/4 , (3(4) + 1(10)/4
(x,y) = (-9+ 5)/4 , (12 + 10)/4
(x,y) = (-1, 5.5)
<span>3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745............................................................................</span>
The length (L) of the rectangle can be written as a function of the width (W)
![L = 2W - 3](https://tex.z-dn.net/?f=L%20%3D%202W%20-%203)
:
Now since we know Area = Width*Length, we can write the area as a function of the width:
![A = L*W = (2W-3)*W](https://tex.z-dn.net/?f=A%20%3D%20L%2AW%20%3D%20%282W-3%29%2AW)
Distributing the W inside the parentheses we have:
![A = 2W^2 - 3W](https://tex.z-dn.net/?f=A%20%3D%202W%5E2%20-%203W)
We know the area is 54 ft^2, so we can rewrite it as:
![2W^2 - 3W - 54 = 0](https://tex.z-dn.net/?f=2W%5E2%20-%203W%20-%2054%20%3D%200)
Now solve for W by factoring (or by applying the quadratic formula):
![2W^2 - 12W + 9W - 54 = 0](https://tex.z-dn.net/?f=2W%5E2%20-%2012W%20%2B%209W%20-%2054%20%3D%200)
Factor out a common 2W from the first two terms and a 9 from the last two terms:
![2W(W-6) + 9(W-6) = 0](https://tex.z-dn.net/?f=2W%28W-6%29%20%2B%209%28W-6%29%20%3D%200)
Regroup the terms to get our fully factored equation:
![(2W + 9)(W-6) = 0](https://tex.z-dn.net/?f=%282W%20%2B%209%29%28W-6%29%20%3D%200)
This gives us the roots W = 6 and W = -9/2, but width can't be negative so we have width = 6 ft. Then remember that the length L = 2W - 3, so our length is:
![L = 2W - 3 = 2(6) - 3 = 12 - 3 = 9](https://tex.z-dn.net/?f=L%20%3D%202W%20-%203%20%3D%202%286%29%20-%203%20%3D%2012%20-%203%20%3D%209)
So now we know that our rectangle is 9 feet long and 6 feet wide.
This would be 45.9
Get a calculator or try long division :-)