C1 Exam question stuck on

10. PQRS is a rectangle, where P, Q and R are the points (4,9), (2, k) and (8,1) respectively.

a) Find the coordinates of the mid point of PR

b) find the gradient of the line PQ giving your answer in terms of k

c) determine the two possible values of k

d) Find the area of the rectangle PQRS for the case in which PQRS is a square

Okay i can do part A) which is (9-1÷2, 8-4÷2) ie (4,2)

stuck on b c and d any help will be appreciated

Reply 1

steve2005

insparato

.
I don't get the mid-point as (4, 2) I have k as either 3 or 7 I have corrected the labeling of the diagram ( I had Q in two places)

Area of PQRS is 40 ( I hope)

Picture 37.png53.3KB

Picture 38.png32.3KB

Reply 2

lauzy

c) would be ±4 as p and q are at right angles and using the formula lpllqlcospq=pq the angle pq is 90 which is equal to 0, putting the points in would give you this answer.

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for part d) lpl=√97 lql=√65 times these together gives 79.4 or √6305 if you want to keep it in surd form.

Reply 3

insparato

Thanks i didnt understand how to get the midpoint that was my guess just found out how you do it now. Thanks again

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I think the question is abit poor because you could plot PQRS anywhere and thats what i was getting stuck on where the hell are the points....