There

There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie:
a) AB side,
b) height to side c,
c) Axis of the AB side,
d) median ta to side a

Result

p1 = (Correct answer is: p1) Wrong answer
p2 = (Correct answer is: p2) Wrong answer
p3 = (Correct answer is: p3) Wrong answer
p4 = (Correct answer is: p4) Wrong answer

Step-by-step explanation:

a0=2;a1=3 b0=4;b1=1 c0=2;c1=5  p1:ax+by+c=0 c=10   a a0+b a110=0 a b0+b b110=0 a (2)+b 310=0 a 4+b (1)10=0  2a3b=10 4ab=10  a=4 b=6  p1:6x+4y10=0  p1
p2p1;Cp2  n2=(b;a)  p2:n0 x+n1 y+z=0   b c0+a c1+z=0 6 2+4 5+z=0  z=8  p2:6x+4y8=0 p2:6x4y+8=0  p2
S=AB/2 s0=(a0+b0)/2=((2)+4)/2=1 s1=(a1+b1)/2=(3+(1))/2=1  p3:n0 x+n1 y+w=0   b s0+a s1+w=0 6 1+4 1+w=0  w=2  p3:6x+4y+2=0 p3:6x4y2=0  p3
p4=CS   v0 c0+v1 c13=0 v0 s0+v1 s13=0 v0 2+v1 53=0 v0 1+v1 13=0  2v0+5v1=3 v0+v1=3  v0=4 v1=1  p4:4xy3=0 p4



We will be pleased if You send us any improvements to this math problem. Thank you!



avatar




Tips to related online calculators
Line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our trigonometric triangle 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: video1

Related math problems and questions:

  • General line equations
    lines_1 In all examples, write the GENERAL EQUATION OF a line that is given in some way. A) the line is given parametrically: x = - 4 + 2p, y = 2 - 3p B) the line is given by the slope form: y = 3x - 1 C) the line is given by two points: A [3; -3], B [-5; 2] D) t
  • Three parallels
    rs_triangle The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
  • Coordinates
    geodet Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
  • Circle
    kruznica The circle touches two parallel lines p and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
  • Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split the AC side into three equal lines. KLM is an isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  • Touch x-axis
    touch_circle Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
  • Lines
    lines_4 How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line?
  • Isosceles triangle
    rr_triangle3 In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
  • Center
    center_triangle In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
  • MO - triangles
    metal On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB seg
  • Equation of circle 2
    circle_axes Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x.
  • Three points 2
    vectors_sum0 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB, and DC is parallel to AB. Calculate the coordinates of D.
  • On a line
    linearna On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].
  • Line
    lines_1 Write an equation of a line parallel to To 9x + 3y = 8 That Passes Through The Point (-1, -4). Write in form ax+by=c.
  • Equilateral triangle ABC
    equliateral In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont
  • Three points
    triangle_rt_taznice Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out: (a) whether the triangle KLM is right b) calculate the length of the line to the k side c) write the coordinates of the vector LM d) write the directional form of the KM side e) write the d
  • Circle
    circle_ag Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?