WorksheetsCoordinate Proofs
Total questions: 20
Worksheet time: 20mins
Explain why it is convenient to place a right triangle on the grid as shown when writing a coordinate proof.
The hypotenuse of the right triangle is easy to identify.
The side lengths are often easier to find because you are using zeros in your expressions.
It is easier to dilate the figure on the coordinate plane.
Both legs have the same length when you place the triangle on the x- and y-axes.
Write a plan for the proof.
Given: G is the midpoint of HF
Prove: △GHJ≅△GFO
Find the coordinates of G using the Midpoint Formula
Use these coordinates and the Distance formula to show that OG ≅ JG.
Show that HG≅ FG by the definition of midpoint and ∠HGJ ≅ ∠FGO by the Vertical Angles Congruence Theorem.
Find the coordinates of G using the Distance Formula
Use these coordinates and the Midpoint formula to show that OG ≅ JG.
Show that HG≅ FG by the definition of midpoint and ∠HGJ ≅ ∠FGO by the Vertical Angles Congruence Theorem.
Then, use the SAS Congruence Theorem to conclude that △GHJ ≅ △GFO.
Then, use the SSS Congruence Theorem to conclude that △GHJ ≅ △GFO.
You and your cousin are camping in the woods. You hike to a point that is 500 meters east and 1200 meters north of the campsite. Your cousin hikes to a point that is 1000 meters east of the campsite.
The distance from you to your cousin is ______ meters.
1500
1300
1200
1000
How is a coordinate proof different from other types of proofs you have studied?
You do not need to write a plan for a coordinate proof.
You do not have a Given or Prove statement.
You have to assign coordinates to vertices and write expressions for the side lengths and slopes of segments.
You can only do coordinate proofs with triangles.
Lamar is writing a coordinate proof to show that a segment from the midpoint of the hypotenuse of a right triangle to the opposite vertex forms two triangles with equal areas. He starts by assigning coordinates as given.
N is the midpoint of segment KL. Therefore, the coordinates of N are (a, ___)
ab
b
2a
4b
Complete the coordinate proof of the theorem.
Given: ABCD is a square.
Prove: The diagonals of ABCD are perpendicular.
The coordinates of square ABCD A(0, 0), B(____, 0), C(_____, a), and D(0, a).
5 , 4
a, a
1 , -1
a, 1
Complete the coordinate proof of the theorem.
Given: ABCD is a square.
Prove: The diagonals of ABCD are perpendicular.
The slope of segment BD when simplified is equal to -1.
The product of the slopes is equal to
360
0
1
-1
Using coordinate geometry proofs, prove that a quadrilateral with vertices at (0,0), (4,0), (4,3), and (0,3) is a rectangle.
By showing all angles are 90 degrees.
By showing opposite sides are parallel and equal in length.
By showing diagonals bisect each other.
By showing it has four sides.
T (___, ___)
(0, 2a)
(2a, 2a)
(2a, y)
(2a, 0)
C ( (a) , q)
T (a, ___)
b
a
0
b/2
E (___, ___)
(-2g, b)
(-x, 0)
(-2g, 0)
(0, 0)
Write a plan for the proof. Given Coordinates of vertices of △OPM and △ONM Prove △OPM and △ONM are isosceles triangles
Find the lengths of OP, PM, MN, NO and OM to show that △OMP≅△OMN by the SSS Congruence Theorem.
Find the lengths of OP, PM, MN, and NO to show that OP ≅ PM and MN ≅ NO.
Find the coordinates of the vertex O.
(a)
Find the coordinates of the vertex U.
(k, 0)
(0, k)
(k, 2k)
(2k, k)
You and your cousin are camping in the woods. You hike to a point that is 500 meters east and 1200 meters north of the campsite. Your cousin hikes to a point that is 1000 meters east of the campsite.
The distance from the campsite to you is ______ meters.
1500
1300
1200
1000
Find the coordinates of the unlabeled vertices.
(-2h,0)
(2,4k)
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Which set of coordinates is most convenient?
(0,2) , (2,6) , (6,0) , (0,0)
(2,6) , (0,0) , (6,2) , (6,0)
(2,0) , (0,0) , (2,6) , (0,6)
(0,2) , (0,0) , (6,2) , (6,0)
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Which set of coordinates is most convenient?
(0,w) , (w,l) , (w,0) , (0,0)
(0,w) , (0,0) , (l,w) , (l,0)
(w,0) , (0,0) , (w,l) , (0,l)
(0,l) , (0,0) , (l,w) , (w,0)
Find the coordinates of the unlabeled vertices.
(0,0)
(h,0)
