# Unit 8Connecting Algebra and Geometry

## Lesson 1

### Learning Focus

Find the distance between two points in the coordinate plane.

Find the perimeter of a geometric figure in the coordinate plane.

### Lesson Summary

In this lesson, we learned to find the distance between two points. We used the Pythagorean theorem to develop a formula that could be used whenever we need to find the length of a segment between two points. The formula can be applied to find the length of the sides of a geometric figure in the coordinate plane to calculate the perimeter.

## Lesson 2

### Learning Focus

Locate the midpoint of a segment and a point that divides the segment in a given ratio.

### Lesson Summary

In this lesson, we examined strategies for dividing a line segment into two parts that fit a given ratio. One common application of this concept is to find the coordinates of the midpoint of a segment, given the coordinates of the endpoints.

## Lesson 3

### Learning Focus

Recognize parallel and perpendicular lines in a coordinate plane.

Write the equation of a line parallel or perpendicular to a given line through a given point.

### Lesson Summary

In this lesson, we learned criteria for determining if two lines in a coordinate plane are parallel or perpendicular. We also learned how to write equations of lines parallel or perpendicular to a given line through a given point.

## Lesson 4

### Learning Focus

Prove quadrilaterals are parallelograms, rectangles, rhombi, or squares using coordinates.

Find the perimeter and area of a quadrilateral on the coordinate plane.

### Lesson Summary

In this lesson, we used the distance formula, the midpoint rule, and the properties of slopes of parallel and perpendicular lines to determine if a given set of points on a coordinate plane formed the vertices of a parallelogram, rectangle, rhombus, or square. We also found the perimeter and area of figures defined by the coordinates of their vertices.