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**Vedanti****Member**- Registered: 2017-12-19
- Posts: 5

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)*

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,340

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

Children are not defined by school ...........The Fonz

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