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New Further Maths Year 12 Edexcel TB Ex 7C question 12 watch

1. I need help with this question please... Its from the Edexcel Year 12 New Further Maths course book. Exercise 7C question 12...

A triangle T has vertices at the points A = (k,1), B = (4,1) and C = (4,k) where k is an integer constant.

Triangle T is formed by the matrix (4 -1)TOP ROW (k 2) BOTTOM ROW (This is my attempt at typing 2x2)

Given that triangle T has a right-angle at B, and the area of T' is 10, find the value of k.

Here's what I've done... I've sketched the two possible locations of A and the two possible locations of C. What I get is then four possible triangles.

I have considered the dimensions of all four, done BxH/2 = 10/(8 + k) , since (8+k) is the determinant of the matrix and hence the scale factor of enlargement.

In each case, I end up solving a cubic. The only cubic that gives rise to an integer value for k is when I choose the top left triangle, where k ends up = 2

But this seemed like a lot of work for 5 marks.

Am I missing something obvious.

Sorry if what I'm saying makes little sense; if you attempt the question I hope you will see what I mean.

Thank you.
2. The area scale factor of a matrix transformation is ad-bc where it was transformed by the matrix row 1: (a,b) row 2: (c,d) . I can't quite remember if this is a general rule or if there are any conditions to it.
I'm not sure if this will help, but I hope it does.
3. (Original post by beast14)
I need help with this question please... Its from the Edexcel Year 12 New Further Maths course book. Exercise 7C question 12...

A triangle T has vertices at the points A = (k,1), B = (4,1) and C = (4,k) where k is an integer constant.

Triangle T is formed by the matrix (4 -1)TOP ROW (k 2) BOTTOM ROW (This is my attempt at typing 2x2)

Given that triangle T has a right-angle at B, and the area of T' is 10, find the value of k.

Here's what I've done... I've sketched the two possible locations of A and the two possible locations of C. What I get is then four possible triangles.

I have considered the dimensions of all four, done BxH/2 = 10/(8 + k) , since (8+k) is the determinant of the matrix and hence the scale factor of enlargement.

In each case, I end up solving a cubic. The only cubic that gives rise to an integer value for k is when I choose the top left triangle, where k ends up = 2

But this seemed like a lot of work for 5 marks.

Am I missing something obvious.

Sorry if what I'm saying makes little sense; if you attempt the question I hope you will see what I mean.

Thank you.
You can speed things up:

Without considering all the triangles you can say that e.g. the base length is so you can end up with the equation

Then it's not hard to find integer solutions to this since you need a product of positive integers equal to 20. There's no need to expand and solve a cubic.

There may be a nicer way of doing this question but I haven't spent much time on it.

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