Given:
![XR=x+8](https://tex.z-dn.net/?f=%20XR%3Dx%2B8%20)
![RY=4x-10](https://tex.z-dn.net/?f=%20RY%3D4x-10%20)
Since R is the midpoint of the line, we can set XR equal to RY and solve for x.
![RY=XR](https://tex.z-dn.net/?f=%20RY%3DXR%20)
![4x-10=x+8](https://tex.z-dn.net/?f=%204x-10%3Dx%2B8%20)
![4x=x+18](https://tex.z-dn.net/?f=%204x%3Dx%2B18%20)
![3x=18](https://tex.z-dn.net/?f=%203x%3D18%20)
![x=6](https://tex.z-dn.net/?f=%20x%3D6%20)
Now we know what x is. We can plug in x to RY and XR and then add it all together to find XY. Let's find XR:
![XR=6+8](https://tex.z-dn.net/?f=%20XR%3D6%2B8%20)
![XR=14](https://tex.z-dn.net/?f=%20XR%3D14%20)
Let's find RY now:
![RY=4(6)-10](https://tex.z-dn.net/?f=%20RY%3D4%286%29-10%20)
![RY=24-10](https://tex.z-dn.net/?f=%20RY%3D24-10%20)
![RY=14](https://tex.z-dn.net/?f=%20RY%3D14%20)
Since we know that:
![XR+RY=XY](https://tex.z-dn.net/?f=%20XR%2BRY%3DXY%20)
We can plug in our answers:
![14+14=XY](https://tex.z-dn.net/?f=%2014%2B14%3DXY%20)
Final answer:
![XY=28](https://tex.z-dn.net/?f=%20XY%3D28%20)
Answer:
x = 1, y = 7
Step-by-step explanation:
If y = -3x - 4, then
6x -3x -4 = 1
3x - 4 =-1
3x = 3
x = 1
If x = 1, then
y = -3*1 -4 = -3 -4 = -7
Yes, because figure B can be obtained from figure A by a series of translations
The coordinates of point P are: (1/5 , -12/5)
Step-by-step explanation:
Here
R(-3,-4) = (x1,y1)
S(5,0) = (x2,y2)
The ratio is: 2:3
The coordinates of a point that divides the line in ratio m:n are given by:
Let P be the point then
![(x_P, y_P) = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})](https://tex.z-dn.net/?f=%28x_P%2C%20y_P%29%20%3D%20%28%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2C%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%29)
Putting values
![(x_P, y_P) = (\frac{(2)(5)+(3)(-3)}{2+3},\frac{(2)(0)+(3)(-4)}{2+3})\\= (\frac{10-9}{5},\frac{0-12}{5})\\=(\frac{1}{5},\frac{-12}{5})](https://tex.z-dn.net/?f=%28x_P%2C%20y_P%29%20%3D%20%28%5Cfrac%7B%282%29%285%29%2B%283%29%28-3%29%7D%7B2%2B3%7D%2C%5Cfrac%7B%282%29%280%29%2B%283%29%28-4%29%7D%7B2%2B3%7D%29%5C%5C%3D%20%28%5Cfrac%7B10-9%7D%7B5%7D%2C%5Cfrac%7B0-12%7D%7B5%7D%29%5C%5C%3D%28%5Cfrac%7B1%7D%7B5%7D%2C%5Cfrac%7B-12%7D%7B5%7D%29)
Hence,
The coordinates of point P are: (1/5 , -12/5)
Keywords: Coordinate geometry
Learn more about coordinate geometry at:
#LearnwithBrainly