Coordinates of square vertices

The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.

Result

x1 =  -7
y1 =  -1
x2 =  -2
y2 =  2
x3 =  -4
y3 =  -6

Solution:

s0=−3 s1=−2  x0=1 y0=−3  d0=x0−s0=1−(−3)=4 d1=y0−s1=(−3)−(−2)=−1  n⊥d ∣n∣=∣d∣ n.d=0  n0=−d1=−(−1)=1 n1=d0=4  x1=s0−d0=(−3)−4=−7s_{ 0 } = -3 \ \\ s_{ 1 } = -2 \ \\ \ \\ x_{ 0 } = 1 \ \\ y_{ 0 } = -3 \ \\ \ \\ d_{ 0 } = x_{ 0 }-s_{ 0 } = 1-(-3) = 4 \ \\ d_{ 1 } = y_{ 0 }-s_{ 1 } = (-3)-(-2) = -1 \ \\ \ \\ n \perp d \ \\ |n| = |d| \ \\ n . d = 0 \ \\ \ \\ n_{ 0 } = -d_{ 1 } = -(-1) = 1 \ \\ n_{ 1 } = d_{ 0 } = 4 \ \\ \ \\ x_{ 1 } = s_{ 0 }-d_{ 0 } = (-3)-4 = -7
y1=s1−d1=(−2)−(−1)=−1y_{ 1 } = s_{ 1 }-d_{ 1 } = (-2)-(-1) = -1
x2=s0+n0=(−3)+1=−2x_{ 2 } = s_{ 0 }+n_{ 0 } = (-3)+1 = -2
y2=s1+n1=(−2)+4=2y_{ 2 } = s_{ 1 }+n_{ 1 } = (-2)+4 = 2
x3=s0−n0=(−3)−1=−4x_{ 3 } = s_{ 0 }-n_{ 0 } = (-3)-1 = -4
y3=s1−n1=(−2)−4=−6y_{ 3 } = s_{ 1 }-n_{ 1 } = (-2)-4 = -6

Try another example


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...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Following knowledge from mathematics are needed to solve this word math problem:

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. Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.

Next similar math problems:

  1. Vector
    vectors Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
  2. Coordinates of vector
    vectors_2 Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
  3. Vector - basic operations
    vectors_1 There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w.
  4. Vectors
    green For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
  5. Unit vector 2D
    one_1 Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
  6. Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  7. Imaginary numbers
    Complex_conjugate_picture.svg Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
  8. Theorem prove
    thales_1 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?
  9. Scalar product
    vectors_sum0_2 Calculate the scalar product of two vectors: (2.5) (-1, -4)
  10. De Moivre's formula
    sqrt3_complex There are two distinct complex numbers z such that z3 is equal to 1 and z is not equal 1. Calculate the sum of these two numbers.
  11. Skiing
    sneh Ski gondola starts at a distance of 975 m from the top and is 389 meters long. I went to the bottom station to the top station. How many meters I must go to the top of hill?
  12. Floods
    povodne After the floods that hit a school, parents help repair the damage. My father worked at the school 50 hours, my mom 5 hours less. How many hours worked mother? How many hours worked my parents together?
  13. AS - sequence
    matematika_icon What are the first ten members of the sequence if a11=22, d=2.
  14. Airport
    b737 On blue airport are 23 aircraft, flew 7 aircraft, the arrival 9 aircraft. How many planes were a blue airport tonight?
  15. Points collinear
    collinear Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
  16. Line
    img2 Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
  17. ABS
    sphere_nice What is the value of ? ?