# Symmetry by plane

Determine the coordinates of a image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0

Result

x =  1
y =  -2
z =  2

#### Solution:

$r:x-y-4z-13=0 \ \\ A(3,-4,-6) \ \\ \ \\ n=s \ \\ n=(1,-1,-4) \ \\ p: x=t+a; y=-t+b; z=-4t + c; t \in R \ \\ \ \\ 3=t + a \ \\ -4=-t + b \ \\ -6=-4 \cdot \ t + c \ \\ t=1 \ \\ \ \\ a+t=3 \ \\ b-t=-4 \ \\ c-4t=-6 \ \\ t=1 \ \\ \ \\ a=2 \ \\ b=-3 \ \\ c=-2 \ \\ t=1 \ \\ \ \\ p: x=t+2; y=-t-3; z=-4t-2; t \in R \ \\ \ \\ p(t=-1)=A' \ \\ \ \\ x=-1+a=-1+2=1$
$y=-(-1)+b=-(-1)+(-3)=-2$
$z=-4 \cdot \ (-1)+c=-4 \cdot \ (-1)+(-2)=2$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.

## Next similar math problems:

1. Owner of the company
The owner of the company with extensive administrative activity wants to sell the obsolete 3 machines at the price of CZK 1000 per 1 machine with a six-month warranty period. If the machine breaks down during this period, the owner will return the employe
2. Third member
Determine the third member of the AP if a4=93, d=7.5.
3. Equation
Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
4. Circle - AG
Find the coordinates of circle and its diameter if its equation is: ?
5. Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
6. Line
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
7. Line
It is true that the lines that do not intersect are parallel?
8. Reciprocal value
How do I calculate a number x that is 9 greater than its reciprocal (1/x)?
9. Quadratic function 2
Which of the points belong function f:y= 2x2- 3x + 1 : A(-2, 15) B (3,10) C (1,4)
10. Equation of circle
find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
11. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
12. College 2
College student is moving into a dormitory. The student rent a truck for $19.95 plus$0.99 per mile. Before returning the truck the student fills the tank with gasoline, which cost $65.32. Total cost$144.67. Using a linear equation, explain the process t
13. Parametric equation
Find the parametric equation of a line with y-intercept (0,-4) and a slope of -2.
14. Expressions 3
If k(x+6)= 4x2 + 20, what is k(10)=?
15. GP members
The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
16. Asymptote
What is the vertical asymptote of ?
17. Trucks
Three lorries droved bricks. One drove n bricks at once, second m less bricks than the first and third 300 bricks more the first lorry. The first lorry went 4 times a day the largest went 3 times a day and the smallest 5 times a day. How many bricks b