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.

Answer:

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.]

Answer:

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.

Answer:

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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