Coordinates of square vertices

I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.

Result

x2 =  2.97
y2 =  -0.596
x3 =  -1.03
y3 =  -3.596
x4 =  -0.97
y4 =  8.596
x5 =  -4.97
y5 =  5.596

Solution:

x0=3 y0=1  x1=1 y1=4  a=(x0x1)2+(y0y1)2=((3)1)2+(14)2=5  tanα=y0y1x0y1=14(3)4=370.4286  α=arctan(y0y1x0y1)=arctan(14(3)4)0.4049 rad  dx=a cos(α)=5 cos(0.4049)4.5957 dy=a sin(α)=5 sin(0.4049)1.9696  x2=x1+dy=1+1.96962.9696=2.97x_{ 0 } = -3 \ \\ y_{ 0 } = 1 \ \\ \ \\ x_{ 1 } = 1 \ \\ y_{ 1 } = 4 \ \\ \ \\ a = \sqrt{ (x_{ 0 }-x_{ 1 })^2+(y_{ 0 }-y_{ 1 })^2 } = \sqrt{ ((-3)-1)^2+(1-4)^2 } = 5 \ \\ \ \\ \tan α = \dfrac{ y_{ 0 }-y_{ 1 } }{ x_{ 0 }-y_{ 1 } } = \dfrac{ 1-4 }{ (-3)-4 } = \dfrac{ 3 }{ 7 } \doteq 0.4286 \ \\ \ \\ α = \arctan (\dfrac{ y_{ 0 }-y_{ 1 } }{ x_{ 0 }-y_{ 1 } } ) = \arctan (\dfrac{ 1-4 }{ (-3)-4 } ) \doteq 0.4049 \ rad \ \\ \ \\ dx = a \cdot \ \cos(α) = 5 \cdot \ \cos(0.4049) \doteq 4.5957 \ \\ dy = a \cdot \ \sin(α) = 5 \cdot \ \sin(0.4049) \doteq 1.9696 \ \\ \ \\ x_{ 2 } = x_{ 1 } + dy = 1 + 1.9696 \doteq 2.9696 = 2.97
y2=y2=y1dx=44.59570.5957=0.596y_{2} =y_{ 2 } = y_{ 1 } - dx = 4 - 4.5957 \doteq -0.5957 = -0.596
x3=x0+dy=(3)+1.96961.0304=1.03x_{ 3 } = x_{ 0 } + dy = (-3) + 1.9696 \doteq -1.0304 = -1.03
y3=y0dx=14.59573.5957=3.596y_{ 3 } = y_{ 0 } - dx = 1 - 4.5957 \doteq -3.5957 = -3.596
x4=x4=x1dy=11.96960.9696=0.97x_{4} =x_{ 4 } = x_{ 1 } - dy = 1 - 1.9696 \doteq -0.9696 = -0.97
y4=y4=y1+dx=4+4.59578.5957=8.596y_{4} =y_{ 4 } = y_{ 1 } + dx = 4 + 4.5957 \doteq 8.5957 = 8.596
x5=x0dy=(3)1.96964.9696=4.97x_{ 5 } = x_{ 0 } - dy = (-3) - 1.9696 \doteq -4.9696 = -4.97
y5=y0+dx=1+4.59575.5957=5.596  a2=(x0x3)2+(y0y3)2=((3)(1.0304))2+(1(3.5957))25.0004 a3=(x1x2)2+(y1y2)2=(12.9696)2+(4(0.5957))25.0004 a4=(x2x3)2+(y3y2)2=(2.9696(1.0304))2+((3.5957)(0.5957))2=5  b2=(x0x5)2+(y0y5)2=((3)(4.9696))2+(15.5957)25.0002 b3=(x1x4)2+(y1y4)2=(1(0.9696))2+(48.5957)25.0004 b4=(x4x5)2+(y4y5)2=((0.9696)(4.9696))2+(8.59575.5957)25.0002y_{ 5 } = y_{ 0 } + dx = 1 + 4.5957 \doteq 5.5957= 5.596 \ \\ \ \\ a_{ 2 } = \sqrt{ (x_{ 0 }-x_{ 3 })^2+(y_{ 0 }-y_{ 3 })^2 } = \sqrt{ ((-3)-(-1.0304))^2+(1-(-3.5957))^2 } \doteq 5.0004 \ \\ a_{ 3 } = \sqrt{ (x_{ 1 }-x_{ 2 })^2+(y_{ 1 }-y_{ 2 })^2 } = \sqrt{ (1-2.9696)^2+(4-(-0.5957))^2 } \doteq 5.0004 \ \\ a_{ 4 } = \sqrt{ (x_{ 2 }-x_{ 3 })^2+(y_{ 3 }-y_{ 2 })^2 } = \sqrt{ (2.9696-(-1.0304))^2+((-3.5957)-(-0.5957))^2 } = 5 \ \\ \ \\ b_{ 2 } = \sqrt{ (x_{ 0 }-x_{ 5 })^2+(y_{ 0 }-y_{ 5 })^2 } = \sqrt{ ((-3)-(-4.9696))^2+(1-5.5957)^2 } \doteq 5.0002 \ \\ b_{ 3 } = \sqrt{ (x_{ 1 }-x_{ 4 })^2+(y_{ 1 }-y_{ 4 })^2 } = \sqrt{ (1-(-0.9696))^2+(4-8.5957)^2 } \doteq 5.0004 \ \\ b_{ 4 } = \sqrt{ (x_{ 4 }-x_{ 5 })^2+(y_{ 4 }-y_{ 5 })^2 } = \sqrt{ ((-0.9696)-(-4.9696))^2+(8.5957-5.5957)^2 } \doteq 5.0002



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




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. Pythagorean theorem is the base for the right triangle calculator. Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

Next similar math problems:

  1. Triangle IRT
    triangles_5 In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
  2. Unit vector 2D
    one_1 Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
  3. Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  4. Hyperbola
    hyperbola Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
  5. Vector 7
    vectors_sum0_1 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
  6. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  7. ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  8. The fence
    latkovy_plot I'm building a fence. Late is rounded up in semicircle. The tops of late in the field between the columns are to copy an imaginary circle. The tip of the first and last lath in the field is a circle whose radius is unknown. The length of the circle chord i
  9. Right
    r_triangle_1 Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
  10. The ditch
    prikop Ditch with cross section of an isosceles trapezoid with bases 2m 6m are deep 1.5m. How long is the slope of the ditch?
  11. Distance
    origin_math Wha is the distance between the origin and the point (18; 22)?
  12. Cards
    cards_2 Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probabi
  13. One side
    angle_incline One side is 36 long with a 15° incline. What is the height at the end of that side?
  14. 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?
  15. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  16. Trigonometry
    sinus Is true equality? ?
  17. Cotangent
    sin_cos If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α.