Asked by Hermione
The gradient of a straight line l1 passing through the points p[3,4] and Q[a,b] is -3/2.A line l2 is perpendicular to l1 and passes through the points Q and R [2,-1]. Determine the values of a and b.
Answers
Answered by
oobleck
AAAaannndd the bot gets it wrong yet again!
Your solution has P and Q being the same point!
You were off to a good start, when you did
(b-4)/(a-3) = -3/2
3a + 2b = 17
Now just do the same with l2:
(-1-b)/(2-a) = 2/3
2a-3b = 7
Now you have the system
3a+2b = 17
2a-3b = 7
so the solution is a=5 and b=1
Check: we have Q = (5,1)
slope m1 = (1-4)/(5-3) = -3/2
slope m2 = (-1-1)/(2-5) = 2/3
Your solution has P and Q being the same point!
You were off to a good start, when you did
(b-4)/(a-3) = -3/2
3a + 2b = 17
Now just do the same with l2:
(-1-b)/(2-a) = 2/3
2a-3b = 7
Now you have the system
3a+2b = 17
2a-3b = 7
so the solution is a=5 and b=1
Check: we have Q = (5,1)
slope m1 = (1-4)/(5-3) = -3/2
slope m2 = (-1-1)/(2-5) = 2/3
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