Math Is Fun Forum

Vedanti

Member

Registered: 2017-12-19

Posts: 7

Homework Problems - Please Help!

1) Let F, G, and H be collinear points on the Cartesian plane such that FG/GH = 1. If F = (a, b) and H = (7a, c), then what is the x-coordinate of G?

2) The points (0,4) and (1,3) lie on a circle whose center is on the x-axis. What is the radius of the circle?

I'm really stuck on these...Can someone help? Thanks in advance!

Last edited by Vedanti (2018-01-17 09:26:03)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Homework Problems - Please Help!

hi Vedanti

Q1.  There will be different numeric answers, depending on the values of a, b and c; so you won't be able to give numeric coordinates for this.  But an answer with a, b and c is possible.

G is the midpoint of FH, and there is a simple formula for its coordinates:

Add together the x coords of F and H and half it.  This is the x coord of G.  y similarly.

Q2. Again there's a formula (for the equation of a circle) that will help here:

where (a,b) is the centre of the circle, and r the radius.

So if you substitute the known values you'll get a pair of simultaneous equations in a and r.  (not b?  why no b?)

So you can work out both (looks like it may be easier to calculate 'a' first).

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob