Another G C S E Question

[kuiperbelt]

The straight line L has equation 3x + 2y = 18
The point A has coordinates (0, 3)
The straight line M is perpendicular to to L and passes through point A.

Line L crosses the y-axist at the point B
Line L and M intersect at the point C

Work out the area of triangle ABC
You must show all your working.

[QuizmasterG]

Are these for fun or are you getting answerers to do your homework for you?

[bobbinwales]

Equation of L is y = (2/3)x + 3 if my memory is as good as I hope.
That's s starter for you/ him

[Etch]

Line L crosses the x-axis at (6,0), call this point D, and the y-axis at (0,9), point B. If the origin (0,0) is point O then for right-angled triangle DBO, OD is of length 6 and OB is of length 9. Its area is therefore (6 x 9)/2 = 27 and the length of BD (its hypotenuse) = √(6² + 9²) = √(36 + 81) = √117 = 3 x √13

Triangle ABC is similar to triangle DBO because they are both right-angled and have angle ABC in common. ABC's hypotenuse (AB) is of length 6 (difference in y-coordinates of B and A), so the dimensions of triangle ABC are 6/(3 x √13) = 2/√13 times the dimensions of triangle DBO. The area of triangle ABC is therefore (2/√13)² times the area of triangle DBO. So

Area of triangle ABC = (2/√13)² x 27 = (4/13) x 27 = 108/13 ≈ 8.3

Here's a diagram in case you're struggling to visualise the situation: https://ibb.co/cFzqzX9

Amazing how useful 'similar triangles' can be, isn't it? Saves having to formulate the equation of line M and solve for the coordinates of point C.

[bobbinwales]

Well I got 108/13 without any pythagoras or similar triangles.
Just found where the lines crossed at (36/13,63/13) and then did area of triangle formula (6 x36/13)/2...

I wandered whether all this stuff would come in useful someday

[kuiperbelt]

F.A.O QuizmasterG

This is for my grandson. He is determined to get a grade 8/9 in his GCSE math. He has a bunch of past exam papers dating back to 2014 accompanied with mark scheme answers.
The problem is best described from the 2 links below, question and mark scheme respectively.
I think you'll agree (in some cases) the mark scheme answer is not enlightening and does not help the child to progress.

https://ibb.co/YdwTDYR

https://ibb.co/SnCkkSg

Also my grandson will not be 16 until very late August. One of his class mate's will be 17 in early September, making him very nearly one year older. I just think my grandson is disadvantaged because of his very late B'day. His 'brain development' is playing catch up with some of the other pupils!!

[bednobs]

or you could argue he's had a whole year more of schooling than his peer?

[MargoTester]

It's always been that way, my birthday is 1st August and my friend's is the 29th making us among the youngest in our year. The thing is that you all get the same amount of tuition

[Zacs-Master]

'His 'brain development' is playing catch up with some of the other pupils!!'

Assuming ever single teenager develops at the same rate.