need help a few math problems

1.The three points (3, 6), (4, 6) and (4, 8) are reflected in the line 3x + 4y = 50 to give three of the vertices of a parallelogram. The parallelogram is completed in such a way that the additional vertex P is as far from the origin as possible.
What are the coordinates of P?
2. The two parabolas y = x ^2 + 5x + 2 and x = y^2 + 5y + 2 intersect in four points, with two of these intersections lying on the line y = x.
Find the area of the polygon formed by joining the four points of intersection.
3. A circle of radius 1 rolls along the positive x-axis towards the origin until it is stopped by the line y = x.
What are the coordinates of its centre now?

Please read the rules and post what you've done. TSR is not a homework service

im sorry its my transition work for alevel and ive never been taught any of this and i dont know where to start

Draw a diagram for the first one then post it.

I have done it on my pc on GeoGebra but it wont let me upload a screenshot

Download and upload it using the camera symbol. Anyway you should be able to do the question now.

(Original post by Muttley79)

i dont understand what the question is actually asking me and whenever i try to it says "error uploading attachment please try again"

If you can't upload the image to TSR, upload it to an image hosting site and post a link (TSR is often a bit rubbish about image attachments).

As far as the problem goes, the first step is to reflect the given 3 points in the given line. Have you done this yet?

If you can't upload the image to TSR, upload it to an image hosting site and post a link (TSR is often a bit rubbish about image attachments).

As far as the problem goes, the first step is to reflect the given 3 points in the given line. Have you done this yet?

i’ll try that and yeah i’ve reflected it on the line i just don’t know where i go from there

You must be able to add the 4th point which makes a rectangle, then reflect it?
Or add the exta point to the reflected points, by picking one of the end points then adding on the "opposite side".

does it matter where it goes? i didn't know whether i had to work something out to figure out the final point

If you form the not rflecgted parallelogram with the extra point closest to the origin, the reflected point will be furthest from the origin. As non reflected C is furthest from the origin, the non refllected D must join with A and B so its reflection ...

https://ibb.co/BCd2MR9 does this seem right?

Not really your added (reflected) point is close to the origin, not far away.

Its the same pic? As previous, the point D should connect with A and B. Not reflected D will be close to the origin. Relfected D will be far from the origin.

on the second one B is the point i added

It seems like one of ther points moved as well as there is no point at (4,6). Assming you have the three given points A,B,C why not think about how you could add a D connecting to
A,B
A,C
B,C
and decide which one of the three (reflected) is furthest from the origin. Thats what the question asks.