c) Given P (1, 2) and S (-3,0) P divides OQ
in the ratio 2:3 and OPRS is a parallelogram,
Find:
XP(2.2)
:
S
-3,0
i) the coordinates of Q
ii) the co-ordinates of R
iii) the equation of a line through P parallel to
the y-axis
Answers
i) the coordinates of Q = (5/2 , 5) , ii) the co-ordinates of R = (-2 , 2) , iii) x = 1
Step-by-step explanation:
P divides OQ in the ratio 2:3
O (0 , 0)
P ( 1, 2)
Q = ( x , y)
=> 1 = (2x + 3*0)/(2 + 3) & 2 = (2y + 3 * 0)/(2 + 3)
=> 1 = 2x/5 & 2 = 2y/5
=> x = 5/2 & y = 5
=.> Q = (5/2 , 5)
i) the coordinates of Q = (5/2 , 5)
Slope of OP = (2 - 0)/(1 - 0) = 2
Coordinates of R = ( x , y)
Slope RS = y/(x + 3) = 2
=> y = 2x + 6 = 2(x + 3)
Length of OP = √5
Length of RS = √y² + (x + 3)²
y² + (x + 3)² = 5
=> (2(x + 3))² + (x + 3)² = 5
=> (x + 3)² = 1
=> x + 3 = 1
=> x = -2
y = 2
the co-ordinates of R = (-2 , 2)
iii) the equation of a line through P ( 1 , 2) parallel to the y-axis
=> x = 1
Learn more:
The portion of a line intercepted between the coordinate axes
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