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?

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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.