Geometry Problems of the Day (Geometry Regents, June 2011)

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 2011

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


32. A pentagon is drawn on the set of axes below. If the pentagon is reflected over the y-axis, determine if this transformation is an isometry.

Justify your answer. [The use of the set of axes below is optional.]

Answer:

An isometry doesn't change the figures size or shape. The orientation may change.

A reflection across the y-axis will change the orientation but not its size or shape. Therefore, this rigid transformation is an isometry.

33. In the diagram below of △ABC, D is a point on AB, E is a point on BC, AC || DE , CE = 25 inches, AD = 18 inches, and DB = 12 inches. Find, to the nearest tenth of an inch, the length of EB.

Answer:

The triangles are similar because the corresponding angles along the transversals of the parallel lines are congruent. That means the sides are proportional.

EB / DB = CB / AB

EB / 12 = (25 + EB) / (18 + 12)

30 EB = 12(25 + EB)

30 EB = 12 EB + 300

18 EB = 300

EB = 16.666...

EB is 16.7 inches.

34. In circle O, diameter RS has endpoints R(3a,2b − 1) and S(a − 6,4b + 5). Find the coordinates of point O, in terms of a and b. Express your answer in simplest form.

Answer:

Point O is the midpoint of diameter RS.

O( (3a + a - 6) / 2 , (2b - 1 + 4b + 5) / 2)

O ( (4a - 6) / 2 , (6b + 4) / 2)

O ( 2a - 3, 3b + 2)

End of Part II.

More to come. Comments and questions welcome.

More Regents problems.

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