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finding the slope of the line...

Attachment 22532

this problem is taken from dr chung sat math book. im supposed to find the slope of the line. i thought perhaps i could subtract the two x values to find the distance of 15. i just cant figure out how to get the height of the triangle.

let me back up, i want to create a triangle and let the hypotenuse be the slope of the line, which i could find using Pythagorean theorem. want to connect the centers of the circles to form a triangle and then solve...any thoughts on how i could find the height? and solve the problem?

Re: finding the slope of the line...

From the diagram you can see that the radius of the first circle is 5, and the question tells you that the radius of the second circle is twice that. The "height" of the triangle will be the difference between the radius'. Since the radius of the larger circle is twice the radius of the first circle, the height will simply be the radius of the first circle (R = r + r, R - r= r).

Re: finding the slope of the line...

ok so the answer is 1/3. thanks again

Re: finding the slope of the line...

Well, you know centers are (5,5) and (20,10);

so slope = (10 - 5) / (20 - 5) = 5/15 = 1/3.

Isn't that simpler than finding line lengths?