## Tuesday, October 26, 2021

### 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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