# 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.

Correct result:

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

#### Solution:

$s_{0}=-3 \ \\ s_{1}=-2 \ \\ \ \\ x_{0}=1 \ \\ y_{0}=-3 \ \\ \ \\ d_{0}=x_{0}-s_{0}=1-(-3)=4 \ \\ d_{1}=y_{0}-s_{1}=(-3)-(-2)=-1 \ \\ \ \\ n \perp d \ \\ |n|=|d| \ \\ n . d=0 \ \\ \ \\ n_{0}=-d_{1}=-(-1)=1 \ \\ n_{1}=d_{0}=4 \ \\ \ \\ x_{1}=s_{0}-d_{0}=(-3)-4=-7$
$y_{1}=s_{1}-d_{1}=(-2)-(-1)=-1$
$x_{2}=s_{0}+n_{0}=(-3)+1=-2$
$y_{2}=s_{1}+n_{1}=(-2)+4=2$
$x_{3}=s_{0}-n_{0}=(-3)-1=-4$
$y_{3}=s_{1}-n_{1}=(-2)-4=-6$

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

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Vector
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
• Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
• Vector - basic operations
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
• Vectors
For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
• The modulus
Find the modulus of the complex number 2 + 5i
• Parallel and orthogonal
I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w
• Imaginary numbers
Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
• Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
• Scalar product
Calculate the scalar product of two vectors: (2.5) (-1, -4)
• Skiing
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?
• Floods
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?
• Vector equation
Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent
• Airport
On blue airport are 23 aircraft, flew 7 aircraft, the arrival 9 aircraft. How many planes were a blue airport tonight?
• AS - sequence
What are the first ten members of the sequence if a11=22, d=2.
• De Moivre's formula
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.
• ABS
What is the value of ? ?