Coordinate axes

Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.

Correct result:

S =  40.5

Solution:

7x+7y+63=0  x=0: 7 0+7y+63=0 7y=63 y=63/7=9   y=0: 7x+7 0+63=0 7x=63 x=63/7=9   a=x=9=9 b=y=(9)=9  ABC:(0,0),(0,9),(9,0)  S=a b/2=9 9/2=812=40.5-7x + 7y + 63=0 \ \\ \ \\ x=0: \ \\ -7 \cdot \ 0+7y + 63=0 \ \\ 7y=-63 \ \\ y=-63 / 7=-9 \ \\ \ \\ \ \\ y=0: \ \\ -7x+7 \cdot \ 0 + 63=0 \ \\ 7x=63 \ \\ x=63 / 7=9 \ \\ \ \\ \ \\ a=|x|=|9|=9 \ \\ b=|y|=|(-9)|=9 \ \\ \ \\ ABC: (0,0), (0,-9), (9,0) \ \\ \ \\ S=a \cdot \ b / 2=9 \cdot \ 9 / 2=\dfrac{ 81 }{ 2 }=40.5



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!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




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.
See also our right triangle calculator.
Do you want to convert length units?
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Coordinates of vector
    vectors_2 Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
  • Unit vector 2D
    one_1 Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
  • 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
  • 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.
  • Center
    triangle_axis Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
  • The farmer
    field_2 The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine t
  • Medians and sides
    3angle Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
  • Compute 4
    14-12-12 Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
  • Three points
    abs1_1 Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
  • Vertices of a right triangle
    right_triangle_5 Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
  • Centre of mass
    centre_g_triangle The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
  • Distance
    origin_math Wha is the distance between the origin and the point (18; 22)?
  • Vertices of RT
    RightTriangleMidpoint_3 Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
  • Spruce height
    stromcek_7 How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
  • Cable car
    lanovka Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
  • Triangle P2
    1right_triangle Can triangle have two right angles?
  • Distance between 2 points
    axes2 Find the distance between the points (7, -9), (-1, -9)