Geometry Problems of the Day (Geometry Regents, June 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, June 2012

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


32. Using a compass and straightedge, construct the bisector of ∠CBA. [Leave all construction marks.]

Answer:

From ∠CBA, draw an arc that intercepts both BA and BC. Next, from each of those new points on BA and BC, make an arc the same size as the first one. Make a point where these last two arc intersect. Draw the angle bisector from B through this point.

If you used the wrong angle, you can still get one credit.

33. The cylindrical tank shown in the diagram below is to be painted. The tank is open at the top, and the bottom does not need to be painted. Only the outside needs to be painted. Each can of paint covers 600 square feet. How many cans of paint must be purchased to complete the job?

Answer:

You need to find the lateral area of the cylinder. Then divide that by 600 and round up.

Lateral Area = 2 π r h = (2)(3.141592)(12)(22) = 1658.76

Cans of paint = 1658.76 / 600 = 2.76... = 3 cans

In problems like this, you always need to round up because if you round down, you won't have enough paint.

34. On the set of axes below, graph the locus of points that are 4 units from the line x = 3 and the locus of points that are 5 units from the point (0,2). Label with an X all points that satisfy both conditions.

Answer:

The locus 4 units from x = 3 are two vertical lines, four units away on either side. The locus around (0, 2) is a circle with radius 5, with (0,2) as its center.. So angle 2 is 180 - 90 - 63 = 27 degrees.

The circle with intersect the left vertical line in two places. Since it has a radius of 5, it won't intersect the line x = 7 (which is the right vertical line).

End of Part II.

More to come. Comments and questions welcome.

More Regents problems.

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