Algebra Question Solved | Quick and Easy Solution

[tycoga8118]

Sorry, I posted too soon. I was able to figure it out.

 

[Mark44]

Homework Statement

Matt is remodeling the front entrance to his home and needs to cut an arch for the top of an entranceway. The arch must be 8 ft wide and 2 ft high. To draw the arch, he will use a stretched string with chalk attached at an end as a compass.
a) using a coordinate system, locate the center of the circle.
b) What radius should Matt use to draw the arch?

Homework Equations

d=sqrt of ((xsub2-xub1)^2 + (ysub2-ysub1)^2)

The Attempt at a Solution

I did the rest of the chapter and am just stuck on this one. 2 feet high would be point (0,2). 8ft wide would be coordinates (-4,0) and (0,-4).

The point on the right would be at (4, 0), not (0, -4).

So, I don't know what to do to figure out the center. At first, I assumed 8ft wide would mean a radius of 5. But, that's not right. I guess that's because the width of the arch isn't the same thing as two points being on opposite sides of the circle? So I can't just find their midpoint and call that the center because that isn't the actual center of the circle.

I thought about trying to make it a triangle and use Pythagorean's Theorem somehow. but, I'm a little lost at what I'd actually be trying to solve and how that would give me the center of the circle.

You have three points on your circle; namely (-4, 0), (0, 2), and (4, 0). The equation of the circle would be $(x - a)^2 + (y - b)^2 = R^2$. If you substitute the three known points into this equation, you should be able to get three more equations in the parameters a, b, and R. The center of the circle will be at (a, b) and its radius will be R.