1. Warm up
What is the equation of the line that goes through (1, 4) and (5, 12)?
What is the distance between (1, 4) and (5, 12)?
What is the equation of the line that is parallel to #1 and goes through (0, -1)?
What is the equation of the line that is perpendicular to the line in #1 and goes through (0, -1)?

2. Questions over hw?

3. Coordinate Geometry Proofs
Plot the points.
Look for key words to determine whether to use the distance formula or slope formula.
Two pairs of opposite sides that are parallel
- Find the slopes of all four sides… opposite sides have the same slopes.
With four right angles
Find the slopes of all four sides… consecutive lines have perpendicular slopes.
With all sides congruent
- Use the distance formula or Pythagorean theorem to show all the sides have the
same length.
Diagonals in a rhombus are perpendicular
find the slope of diagonals to show they are opposite reciprocals.

4. Example 1: The coordinates of triangle BCD are B(4, 2), C(0, 2), and D(2, 4). Prove that the triangle is an isosceles triangle.
1. What is the question asking you about?
Parallel OR Perpendicular OR Distance
2. BC=
CD=
DB=
3. Is triangle BCD isosceles? How do you know?

5. Example 2: The coordinates of triangle ABC are A(-1, 3), B(5, 5), and C(4, -2). Prove that the triangle is an equilateral triangle.
1. What is the question asking you about?
Parallel OR Perpendicular OR Distance
2. AB=
BC=
CA=
3. Is triangle ABC equilateral? How do you know?

6. Example 3: A rectangle has two pairs of opposite sides that are congruent. Quadrilateral MIKE has vertices M(4, 1), I(6, 4), K(12, 0), and E(10, -3). Prove that Quadrilateral MIKE is a rectangle.
1. What is the question asking you about?
Parallel OR Perpendicular OR Distance
2. MI=
IK=
KE=
EM=
3. Is MIKE a rectangle? How do you know?

7. Example 3b: A rectangle has 4 right angles
Example 3b: A rectangle has 4 right angles. Quadrilateral MIKE has vertices M(4, 1), I(6, 4), K(12, 0), and E(10, -3). Prove that Quadrilateral MIKE is a rectangle.
1. What is the question asking you about?
Parallel OR Perpendicular OR Distance
2. MI=
IK=
KE=
EM=
3. Is MIKE a rectangle? How do you know?

8. Example 4: A square has four congruent sides
Example 4: A square has four congruent sides. Quadrilateral DIAN has vertices D(0, 5), I(3, 6), A(4, 3), and N(1, 2). Prove that Quadrilateral DIAN is a square.
1. What is the question asking you about?
Parallel OR Perpendicular OR Distance
2. DI=
IA=
AN=
ND=
3. Is DIAN a square? How do you know?

9. Example 4b: A rhombus has perpendicular diagonals
Example 4b: A rhombus has perpendicular diagonals. Quadrilateral DIAN has vertices D(0, 5), I(3, 6), A(4, 3), and N(1, 2). Prove that Quadrilateral DIAN is a rhombus.
1. What is the question asking you about?
Parallel OR Perpendicular OR Distance
2. DI=
IA=
AN=
ND=
3. Is DIAN a square? How do you know?

10. Practice Worksheet