Question 10 - 11th Grade Coordinate Geometry Question

[Sufficient_Front_355]

Okay so with F coordinates(unknown) and H coordinates (5,-T) we can't exactly do anything. I know that the gradient of the perpendicular line is 2 but what do I do next?

 

[Dr.Peterson]

Okay so with F coordinates(unknown) and H coordinates (5,-T) we can't exactly do anything. I know that the gradient of the perpendicular line is 2 but what do I do next?

You haven't mentioned finding the coordinates of G. You also seem to be forgetting that with algebra, you can always give a name to something unknown, and do things with it!

Suppose the coordinates of F are (a, b). The fact that it is on the given line provides one equation in a and b; the fact that the line HF has slope 2 gives you another. Solve, and you can express a and b in terms of the parameter T.

 

[Sufficient_Front_355]

I've tried almost all the substitution methods, and nothing worked. So if you could elaborate further it would be very helpful. As for mentioning the coordinates of G thing, it's mentioned in the picture. It doesn't explicitly say to find G but I'm pretty sure you need it to solve this question. Thank you for your time so far

 

[Dr.Peterson]

I've tried almost all the substitution methods, and nothing worked. So if you could elaborate further it would be very helpful. As for mentioning the coordinates of G thing, it's mentioned in the picture. It doesn't explicitly say to find G but I'm pretty sure you need it to solve this question. Thank you for your time so far

Please show me your actual work, so I can see whether you have the wrong equations or the wrong method or a silly mistake.

If you do as I suggested, you will need G in order to find E, but not until then. And it's easy.

 

[Sufficient_Front_355]

So there was a mistake in printing, T is supposed to be 7. So -T = -7. Thanks for your help and time.

 

[Dr.Peterson]

So there was a mistake in printing, T is supposed to be 7. So -T = -7. Thanks for your help and time.

That will help, if the idea of the answer being a function of T was your main problem! I'd actually wondered at first if that was a 7, though it was clearly printed as T.