Evidence of Understanding

**analyze distance in the coordinate plane and use distance to relate points and lines**- calculate the distance between two points using the Pythagorean Theorem
- generalize methods for determining the distance between two coordinate points
- derive the
**distance formula**using a right triangle and the Pythagorean Theorem

- derive the
- explain how the distance formula and Pythagorean Theorem can both be used to find length measurements of segments (or sides of a geometric figure)
**partition**a segment using any point on the segment and find the ratio of its parts- describe connections between the partition ratio, dilation, and scale factor
- given a specified ratio, find the coordinates of a point that partitions a line segment

- find the coordinates of a segment’s
**midpoint**- prove the midpoint of a segment creates two congruent lengths
- recognize that partitioning a segment with its midpoint bisects the segment in a 1:1 ratio

**describe direction in the coordinate plane and use direction to relate points and lines**- given two points, determine the
**direction**of the line containing the two points - generalize methods for determining the direction between two coordinate points
- generate and describe the
**slope formula**using a right triangle

- generate and describe the
- dilate a line segment or line and analyze connections between the pre-image and its image
- make conjectures and use tools to prove
**parallel**lines have the same slope - describe connections between parallel lines, dilation, and scale factor

- make conjectures and use tools to prove
- rotate a line and analyze the relationship between the slope of the original line and its image
- show if slopes of two lines have a product of negative one, then they are
**perpendicular**

- show if slopes of two lines have a product of negative one, then they are
- identify and justify if two lines are parallel or perpendicular
- create equations that represent parallel lines or perpendicular lines
- given the equation of a line and a specified transformation, determine the equation of its image or pre-image on the coordinate plane

- given two points, determine the

Develop conceptual understanding:

distance formula, partition, midpoint, direction, slope formula, parallel, perpendicular

Supporting terms to communicate:

Pythagorean Theorem, ratio, bisect, dilation, scale factor, similarity, proportion, reciprocal, congruent, rotation