Area of a rectangle
What is the area of the rectangle? Continue reading
Triangle area formulas: two case studies in “the shape of the answer”
STEP 2/2012/7
STEP 2/2011/5
STEP 1/2016/6
STEP 2/2017/8
STEP 2/2009/8
The non-collinear points A, B, C have position vectors a, b, c respectively. The points P and Q have position vectors p and q, respectively, given by
p = λ a + (1 − λ)b
q = μ a + (1 − μ)c
where 0 < λ < 1. Draw a diagram showing A, B, C, P and Q
Given that CQ.BP = AB.AC, find μ in terms of λ, and show that, for all values of λ, the line PQ passes through the fixed point D, with position vector d given by
d = − a + b + c
What can be said about the quadrilateral ABDC?
STEP 2/2008/8
The points A and B have position vectors a and b, respectively, relative to the origin O. The points A, B, and O are not collinear. The point P lies on AB between A and B such that
Write down the position vector of P in terms of a, b, and λ
Given that OP bisects the angle AOB, determine λ in terms of a and b, where
a = |a| and b = |b|
The point Q also lies on AB between A and B, and is such that AP=BQ. Prove that
OQ2 − OP2 = (b-a)2
John Conway 1937-2020
John Conway, one of the best-known mathematicians of our day, died on 11 April 2020 from complications from Covid-19. Continue reading
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