Regents Exam Questions G.G.69: Triangles in the Coordinate Plane
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Name: __________________________________
G.G.69: Triangles in the Coordinate Plane: Investigate, justify, and apply the
properties of triangles in the coordinate plane, using the distance, midpoint, and
slope formulas
1 If the vertices of
1) right
2) scalene
3) isosceles
4) equilateral
are
2 Triangle ABC has vertices
1) equilateral
2) isosceles
3) right
4) scalene
,
,
, and
, and
, then
. The triangle may be classified as
3 Which type of triangle can be drawn using the points
1) scalene
2) isosceles
3) equilateral
4) no triangle can be drawn
4 The vertices of
about the angles of
1)
2)
3)
4)
are
is classified as
,
, and
?
and
Which conclusion can be made
, and
. Find the length of
?
5 Triangle ABC has vertices at
simplest radical form.
,
in
Regents Exam Questions G.G.69: Triangles in the Coordinate Plane
Page 2
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Name: __________________________________
6 Triangle ABC has coordinates
,
, and
. Find the perimeter of the
triangle. Express your answer in simplest radical form. [The use of the grid below is
optional.]
7 Given:
,
,
Prove:
is an isosceles right triangle.
[The use of the grid is optional.]
Regents Exam Questions G.G.69: Triangles in the Coordinate Plane
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1 ANS: 3
.
2
3
4
5
REF:
ANS:
ANS:
ANS:
ANS:
011328ge
2
2
1
.
REF: 061115ge
REF: 081226ge
REF: fall0809ge
REF: 061331ge
6 ANS:
REF: 060936ge
7 ANS:
To prove that
is a right triangle, prove that its legs are perpendicular by showing
their slopes are opposite reciprocals:
To prove that
formula:
REF: 011029b
is an isosceles triangle, prove that it legs are congruent by using the distance