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The grid for this problem is used for graphing lines and plotting points and each little square is sort of used as a measurement. t

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In problem 35 of the most recent january geometry regent the student is instructed to use a coordinate plane to graph a triangle and then transform that triangle into a parallelogram. a coordinate plane is a plane spanned by the x and y axis.
a coordinate plane also turns a geometry problem into an algebra problem

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In order to prove that quadrilateral PART is a parallelogram we need to prove that the pairs of opposite sides are parallel and congruent to each other.

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The problem states, "Prove that 'Triangle PAT' is an isosceles triangle." We must use any method to show that two sides of the triangle PAT are equal. So we can use the Pythagorean Theorem to show that segment PA and segment AT have the same distance. Another option could be to use grid paper to clarify the lengths of segment PA and segment AT

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Today in class today, we each received a part of a regents problem. I was given the outside information; whatever was in bold print. One was the instructions. The instructions were saying the whole problem is worth six points; which makes it a hard problem. We have to display all steps, such as diagrams, graphs, etc to show how we reached our answer. You would receive one credit for a correct numerical setup, but with no work. The next thing that was in bold print said "Question 35 is continued on the next page." This means that there is more to the question, that you have not finished the problem yet.

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The use of the set of axes on the next page is optional. If you need additional help, the axes on the next page will give you more assistance to help you solve the problem. Since the question is asking you to prove that triangle PAT is an isosceles triangle, you can use the set of axes on the next page to show your work in order to back up your proof. Using the axes will provide a visual representation of your claim and the triangle. Mr. Williams strongly recommends that you should use the graph to show that you know what the problem is asking you. Doing this will show you understand and we can also analyze further.

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The vertices of a triangles is the point where 2 sides of the triangles meet at the vertex.

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In today's class we were given a problem from the January 2017 geometry regents. The problem first asked us to plot points PAT on a graph and prove that the triangle is an isosceles. In order to do this we needed to prove that segments PA and AT have the same side lengths. After using the Pythagorean theorem

In order to find the coordinates of R so that quadrilateral PART is a parallelogram I did a vector shift of PT where point P maps onto point A. After doing this it could be found that (2,9) is the location of point R.

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"Part IV" means that this is one of the highest value problems on the end of year Regents exam. Problems in this section usually break down into multiple steps. If you can't answer the whole problem, you can usually get a piece of it, resulting in a partial score.