Let , coordinate of points are P( h,k ).
Also , k = 3h + 1
Distance of P from origin :
![d=\sqrt{h^2+k^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7Bh%5E2%2Bk%5E2%7D)
Distance of P from ( -3, 4 ) :
![d=\sqrt{(h+3)^2+(k-4)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28h%2B3%29%5E2%2B%28k-4%29%5E2%7D)
Now , these distance are equal :
![h^2+(3h+1)^2=(h+3)^2+(3h+1-4)^2\\\\h^2+(3h+1)^2=(h+3)^2+(3h-3)^2](https://tex.z-dn.net/?f=h%5E2%2B%283h%2B1%29%5E2%3D%28h%2B3%29%5E2%2B%283h%2B1-4%29%5E2%5C%5C%5C%5Ch%5E2%2B%283h%2B1%29%5E2%3D%28h%2B3%29%5E2%2B%283h-3%29%5E2)
Solving above equation , we get :
![P=(\dfrac{16}{21},\dfrac{23}{7})](https://tex.z-dn.net/?f=P%3D%28%5Cdfrac%7B16%7D%7B21%7D%2C%5Cdfrac%7B23%7D%7B7%7D%29)
Hence , this is the required solution.
Answer:
90 degree rotation in the clockwise direction.
Step-by-step explanation:
Point A transforms to A'
- that is x coordinate: 2 ---> 3
and y coordinate 3 ---> -2
So the rotation is clockwise from Quadrant1 to Quadrant 4.
The slope of OA = 3/2 and the slope of OA' = -2/3.
The product of these slopes = 3/2 * -2/3 = -1 so the lines are perpendicular - that is the line has passed through an angle of 90 degrees.
A similar result occurs if we consider points B, C and D.
<span> Gas station B sells gasoline at a lower rate. Its price is $3.05 per gallon.</span>
Answer:
Step-by-step explanation:
Givens
Number not using given app = 71
Total number of students = 219
% = ?
Solution
P(~given app) = 71 / 219
P(~given app) = 0.324
% = 0.324 * 100 = 32.4%
Answer
32.4% do not use Given App