Question

unit 1 lesson 2 additional practice problems additional practice problem set 5. this diagram was created by starting with points x and y and using only straightedge and compass to construct the rest. circle z has the same radius as circle x. all steps of the construction are visible. describe precisely the straightedge and compass moves required to construct circle z.

Explanation:

Step1: Connect points X and Y

Use straightedge to draw line - segment \(XY\).

Step2: Set compass width

Set the compass width to the distance between \(X\) and \(Y\).

Step3: Place compass at Y

With the compass placed at point \(Y\), draw an arc.

Step4: Locate point Z

The point where the arc intersects the extension of line - segment \(XY\) (beyond \(Y\)) is point \(Z\).

Step5: Construct Circle Z

With the compass width still set to the distance between \(X\) and \(Y\) (which is the radius of Circle \(X\) and should be the radius of Circle \(Z\) as well), place the compass at point \(Z\) and draw a full - circle. This is Circle \(Z\).

Answer:

1. Use straightedge to draw line - segment \(XY\).
2. Set compass width to \(XY\).
3. Place compass at \(Y\) and draw an arc.
4. Locate point \(Z\) as the intersection of the arc and the extension of \(XY\) beyond \(Y\).
5. Place compass at \(Z\) with the same width and draw a circle.