## Thursday, June 09, 2016

### Daily Regents: Coordinate Geometry (June 2015)

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams next week. At least, that is the plan.

### Geometry, June 2015, Questions 27

27. The coordinates of the endpoints of AB are A(-6, -5) and B(4, 0). Point P is on AB.
Determine and state the coordinates of point P, such that AP:PB is 2:3.
[The use of the set of axes below is optional.]

You could solve this by graphing or algebraically. (Algebra shows up in Geometry all the time!)

A ratio of 2:3 means 2/5ths and 3/5ths of the line.
The difference in the x-coordinates is 10. Two-fifths of 10 is 4, and -6 + 4 is -2, the x coordinate for P.
The difference in the y-coordinates is 5. Two-fifths of 5 is 2, and -5 + 2 is -3, the y coordinate for P.

P is at (-2, -3).

See image below for details.

Any questions?

If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.

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