COMEDK2023Evening ShiftMathematicsThree Dimensional GeometryActual
P is a point on the line segment joining the points (3,2,-1) and (6,2,-2) . If the x co ordinate of P is 5 , then its y coordinate is
Options
- A-1
- B2
- C-2
- D1
Correct answer
B. 2
Step-by-step solution
Let the points be A(3, 2, -1) and B(6, 2, -2) . Let P(x, y, z) be a point on the line segment AB such that P divides AB in the ratio k:1 . Using the section formula, the coordinates of P are given by: x = k(6) + 1(3) k+1 , y = k(2) + 1(2) k+1 , z = k(-2) + 1(-1) k+1 Given that the x -coordinate of P is 5 , we have: 5 = 6k + 3 k+1 5(k+1) = 6k + 3 5k + 5 = 6k + 3 k = 2 Now, substitute k = 2 into the expression for the y -coordinate: y = 2(2) + 1(2) 2+1 = 4 + 2 3 = 6 3 = 2 Answer: 2