Points P and Q trisect the line segment joining the points A(-2,0) and B(0,8) such that P is near to A. Find the coordinates of points P and Q.
Answers
Answer:
P = (-4/3 , 8/3)
Q = (-2/3 , 16/3)
Step-by-step explanation:
Points P and Q trisect the line segment joining the points A(-2,0) and B(0,8) such that P is near to A. Find the coordinates of points P and Q.
AB² = (8-0)² + (0-(-2))²
=> AB² = 64 + 4
=> AB² = 68
AP = AB/3
=> AP² = AB²/9
=> AP² = 68/9
let say equation of line
y = mx + c
m = (8-0)/(0-(-2)) = 4
y = 4x + c
8 = 0 + c
=> c = 8
Equation of line
y = 4x + 8
=> y = 4(x + 2)
let say point P
Px & Py
Py = 4(Px + 2)
AP² = (Px -(-2))² + (Py -0)²
=> AP² = (Px + 2)² + (4(Px+2))²
=> AP² = 17(Px+2)²
AP² = 68/9
=> 17(Px+2)² = 68/9
=> (Px +2)² = 4/9
=> Px +2 = ±2/3
Px = -4/3 or -8/3 (-8/3 is not possible as it is out of range of -2 & 0)
Py = 4(-4/3) + 8 = 8/3
point P = (-4/3 , 8/3)
Point Q will be in middle of point P & B
Q = Qx , Qy
so Qx = (Px + 0)/2 = (-4/3)/2 = -2/3
Qy = (Qx + 8)/2 = (8/3 + 8)/2 = 16/3
Q = (-2/3 , 16/3)
Answer:
The coordinates of p is ( -4/3 , 8/3 )
The coordinate of q is ( -2/3 , 16/3 )
