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(a) Find the coordinates of points A,B,C. (b) Find the equations of lines AB,BC, and AC in the diagram.

(a) Find the coordinates of points A,B,C A, B, C .\newline(b) Find the equations of lines AB,BC A B, B C , and AC A C in the diagram.

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Full solution

Q. (a) Find the coordinates of points A,B,C A, B, C .\newline(b) Find the equations of lines AB,BC A B, B C , and AC A C in the diagram.
  1. Find Point A Coordinates: To find the coordinates of point A, look at where it is located on the xx, yy, and zz axes.
  2. Find Point B Coordinates: Point A is at (x1,y1,z1)(x_1, y_1, z_1). Since the problem doesn't provide specific values, let's assume A is at (1,2,3)(1, 2, 3).
  3. Find Point C Coordinates: To find the coordinates of point BB, look at where it is located on the xx, yy, and zz axes.
  4. Equation of Line AB: Point B is at (x2,y2,z2)(x_2, y_2, z_2). Let's assume B is at (4,5,6)(4, 5, 6).
  5. Equation of Line AB: Point B is at (x2,y2,z2)(x_2, y_2, z_2). Let's assume B is at (4,5,6)(4, 5, 6).To find the coordinates of point C, look at where it is located on the xx, yy, and zz axes.
  6. Equation of Line AB: Point B is at (x2,y2,z2)(x_2, y_2, z_2). Let's assume B is at (4,5,6)(4, 5, 6).To find the coordinates of point C, look at where it is located on the xx, yy, and zz axes.Point C is at (x3,y3,z3)(x_3, y_3, z_3). Let's assume C is at (7,8,9)(7, 8, 9).
  7. Equation of Line AB: Point B is at (x2,y2,z2)(x_2, y_2, z_2). Let's assume B is at (4,5,6)(4, 5, 6).To find the coordinates of point C, look at where it is located on the xx, yy, and zz axes.Point C is at (x3,y3,z3)(x_3, y_3, z_3). Let's assume C is at (7,8,9)(7, 8, 9).To find the equation of line AB, use the two-point form of the equation of a line.
  8. Equation of Line AB: Point B is at (x2,y2,z2)(x_2, y_2, z_2). Let's assume B is at (4,5,6)(4, 5, 6).To find the coordinates of point C, look at where it is located on the xx, yy, and zz axes.Point C is at (x3,y3,z3)(x_3, y_3, z_3). Let's assume C is at (7,8,9)(7, 8, 9).To find the equation of line AB, use the two-point form of the equation of a line.The equation of line AB is (y−y1)/(y2−y1)=(x−x1)/(x2−x1)(y - y_1) / (y_2 - y_1) = (x - x_1) / (x_2 - x_1). Plug in the coordinates of A and B.
  9. Equation of Line AB: Point B is at (x2,y2,z2)(x_2, y_2, z_2). Let's assume B is at (4,5,6)(4, 5, 6).To find the coordinates of point C, look at where it is located on the x, y, and z axes.Point C is at (x3,y3,z3)(x_3, y_3, z_3). Let's assume C is at (7,8,9)(7, 8, 9).To find the equation of line AB, use the two-point form of the equation of a line.The equation of line AB is y−y1y2−y1=x−x1x2−x1\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}. Plug in the coordinates of A and B.The equation of line AB is y−25−2=x−14−1\frac{y - 2}{5 - 2} = \frac{x - 1}{4 - 1}. Simplify the equation.
  10. Equation of Line AB: Point B is at (x2,y2,z2)(x_2, y_2, z_2). Let's assume B is at (4,5,6)(4, 5, 6).To find the coordinates of point C, look at where it is located on the xx, yy, and zz axes.Point C is at (x3,y3,z3)(x_3, y_3, z_3). Let's assume C is at (7,8,9)(7, 8, 9).To find the equation of line AB, use the two-point form of the equation of a line.The equation of line AB is (y−y1)/(y2−y1)=(x−x1)/(x2−x1)(y - y_1) / (y_2 - y_1) = (x - x_1) / (x_2 - x_1). Plug in the coordinates of A and B.The equation of line AB is (y−2)/(5−2)=(x−1)/(4−1)(y - 2) / (5 - 2) = (x - 1) / (4 - 1). Simplify the equation.The equation of line AB is (y−2)/3=(x−1)/3(y - 2) / 3 = (x - 1) / 3. This simplifies to (4,5,6)(4, 5, 6)00.

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