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.


29. Triangle TAP has coordinates T(-1,4), A(2,4), and P(2,0). On the set of axes below, graph and label triangle T'A'P', the image of triangle TAP after the translation (x,y) → (x - 5,y - 1).

Answer:

Graph and label TAP. Then plot T', A' and P' by moving 5 boxes to the left and 1 box down. Label them. Then draw triangle T'A'P'.

30. In the diagram below, L || m and QR ⊥ ST at R.

If m∠1 = 63, find m∠2.

Answer:

Using alternate interior angles, you wil have two of the three angles of a triangle and you can find the last one.

Angle QTR is 63 degrees. Angle QRT is 90 degrees. So angle 2 is 180 - 90 - 63 = 27 degrees.

31. Two lines are represented by the equations x + 2y = 4 and 4y - 2x = 12. Determine whether these lines are parallel, perpendicular, or neither. Justify your answer.

Answer:

Find the slope of the two lines.

In standard form, Ax + By = C, the slope of a line is -A/B.

The slope of the first line is -A/B = -1/2.

THe slope of the second line is -A/B = -(-2)/4 = 1/2.

The two lines are neither parallel nor perpendicular.

The slopes are not the same nor are they inverse reciprocals.

If you forgot the formula -A/B, then you could have rewritten the equations in slope-intercept form:

x + 2y = 4
2y = -x + 4
y = -1/2 x + 2

4y - 2x = 12
4y = 2x + 12
y = 1/2 x + 3

More to come. Comments and questions welcome.

More Regents problems.

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