## Saturday, October 16, 2021

### Geometry Problems of the Day (Geometry Regents, August 2012)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

### Geometry Regents, August 2012

Part II: Each correct answer will receive 2 credits. Partial credit is available.

32. The coordinates of the endpoints of FG are (-4,3) and (2,5). Find the length of FG in simplest radical form.

Uset the distance formula or pythagorean theorem.

d = SQRT( (-4 - 2)2 + (3 - 5)2 )
= SQRT( (-6)2 + (-2)2 )
= SQRT( 36 + 4 )
= SQRT(40)
= SQRT(4) * SQRT(10)
= 2 SQRT(10)

33. Using a compass and straightedge, construct a line perpendicular to AB through point P.
[Leave all construction marks.]

We can use the procedure to make a perpendicular bisector that goes through point P. Before we can do that, we need to have a point between A and P that is the same distance away from P as B is. We can measure the distance of PB and make another point on the other side with a little arc.

Next, make an arc above and below P from this new point. Then do the same thing from point B. Finally, connect those two new points, which should line up with P. If they don't line up, then a mistake was made. If this occurs, correct your work. Don't erase. Leave all the marks.

34. The graph below shows the locus of points equidistant from the x-axis and y-axis. On the same set of axes, graph the locus of points 3 units from the line x = 0. Label with an X all points that satisfy both conditions.

The line x = 0 is the y-axis. The locus of points 3 units away would be two vertical lines on either side of the y-axis. That means that there will be four spots that satisfy both conditions.

End of Part II.

More to come. Comments and questions welcome.

More Regents problems.

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