Collinear points and a line that avoids y = 2x
Collinear points and a line that avoids y = 2x
IP 1
7 marks
The points \(A(-2,-1)\), \(B(1,5)\) and \(C(4,11)\) are given.
- By finding the gradients of \(AB\) and \(BC\), show that \(A\), \(B\) and \(C\) lie on one straight line, and find the equation of this line.[3]
- Explain why no point of the form \((k,2k)\) lies on this line.[2]
- Find the point on the line whose \(y\)-coordinate is three times its \(x\)-coordinate.[2]
Solution:
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Answer:(a) \(m_{AB}=m_{BC}=2\) with common point \(B\); \(y=2x+3\) (b) \(2k=2k+3\) gives \(0=3\): \(y=2x\) is parallel to the line (c) \((3,9)\)
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