4.1/4.2 Distance, Midpoint, Slope and Equations

Slides:

Advertisements

Similar presentations

Proving the Distance Formula

Advertisements

1.1 The Cartesian Plane Ex. 1 Shifting Points in the Plane Shift the triangle three units to the right and two units up. What are the three.

7-4A Similar Figures and Proportions Learning Objective: To determine whether two given figures are similar, and to use similarity to find missing lengths.

 A(0, 4)  B(-3, 0)  C(3, 5)  D(-8, -11)  E(7, -5)  F(-3.5, 7.5)

CP Geometry Mr. Gallo. Classifying Polygons in the Coordinate Use three formulas: FormulaWhen to Use it Distance FormulaTo determine whether: Sides are.

10.1 The Distance and Midpoint Formulas What you should learn: Goal1 Goal2 Find the distance between two points and find the midpoint of the line segment.

7.4 Areas of Triangles and Quadrilaterals

Outcome F Quadrilaterals

Formulas to recall Slope: Midpoint: Distance: Definitions to recall Midsegment: Line connecting two midpoints Median: Connects a vertex of a triangle.

Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.

The slope of a line. We define run to be the distance we move to the right and rise to be the corresponding distance that the line rises (or falls). The.

Graphing Quadratics Warm-up (IN) Solve by completing the square Learning Objective: To use completing the square to rewrite a quadratic equation.

Relationships in Geometry Friday January 31st. Objective for today. I understand where we are headed in this unit. I can tell you what we will be covering.

 Calculate the perimeter & area for each figure..

4.7 Triangles and Coordinate Proof

APPLYING POLYGON PROPERTIES TO COORDINATE GEOMETRY 6.7 – 6.8.

The Distance and Midpoint Formulas Goal 1 Find the Midpoint of a Segment Goal 2 Find the distance between two points on a coordinate plane Goal 3 Find.

Section 6-1: Classifying Quadrilaterals March 13, 2012.

Bellwork  Solve for x x-2 5x-13 No Clickers. Bellwork Solution  Solve for x x-2 5x-13.

Solving Exponential Equations

Midpoint and Distance Formulas Goal 1 Find the Midpoint of a Segment Goal 2 Find the Distance Between Two Points on a Coordinate Plane 12.6.

Tests for Parallelograms Advanced Geometry Polygons Lesson 3.

3.6 Pythagorean Theorem Warm-up (IN) 1.Find the area of a square whose sides are 10 units long. 2. The square of what number is 2704? 3. Evaluate each.

6.7 Polygons in the Coordinate Plane

5.5 Quadratic Formula Warm-up (IN) Learning Objective: To use the quadratic formula to find real roots of quadratic equations and to use the roots to find.

1.8: Perimeter, Circumference, and Area

6/4/ : Analyzing Polygons 3.8: Analyzing Polygons with Coordinates G1.1.5: Given a line segment in terms of its endpoints in the coordinate plane,

Polygons In The Coordinate Plane Chapter 6 Section 7.

Polygons in the Coordinate Plane Techniques Examples Practice Problems.

7.1 Classifying Quadrilaterals Warm-up (IN) Learning Objective: to identify quads by using their properties, recognizing the relationships between the.

3.4 Sum and Difference Formula Warm-up (IN) 1.Find the distance between the points (2,-3) and (5,1). 2.If and is in quad. II, then 3.a. b. Learning Objective:

Chapter 6: Quadrilaterals

4.3 Parallels and Perpendiculars Warm-up (IN) Learning Objective: to find the slopes and write equations of parallel and perpendicular lines and to identify.

COORDINATE GEOMETRY Summary. Distance between two points. In general, x1x1 x2x2 y1y1 y2y2 A(x 1,y 1 ) B(x 2,y 2 ) Length = x 2 – x 1 Length = y 2 – y.

Warm-Up Exercises 1.90º 2. 72º Classify each angle as acute, obtuse, or right º 4. How do you know that 1 = 2? ~ 2 1.

5-2B Two-Point Equation of a Line Warm-up (IN) Learning Objective: to determine the equation of a line through 2 given points. Rewrite the equations in.

Aim: Review the distance and midpoint Do Now: in the triangle, find the lengths of two legs (-2,4) (3,6) (3,4)

Special Quadrilaterals

Chapter 9 Review Square RootsTriangles The Pythagorean Theorem Real Numbers Distance and Midpoint Formulas

Find the equation of the line with: 1. m = 3, b = m = -2, b = 5 3. m = 2 (1, 4) 4. m = -3 (-2, 8) y = 3x – 2 y = -2x + 5 y = -3x + 2 y = 2x + 2.

12.4 The Distance Formula Objectives: Use the distance formula to find the distance between 2 points in a coordinate plane. Determine whether a triangle.

Proving Parallelograms: Coordinate Geometry Unit 1C3 Day 4.

7.2/7.3 Parallelograms! Learning Objective: to identify and classify parallelograms and prove that figures are special types of parallelograms. Warm-up.

SLOPE INTERCEPT FORM Y = MX +B SLOPE INTERCEPT FORM WHAT IS THE SLOPE INTERCEPT FORM? Y = MX +B a) M STANDS FOR THE SLOPE (RISE OVER RUN) b) B STANDS.

5-1B Rate of Change Warm-up (IN) Learning Objective: to understand that slope is the rate of change of one quantity relative to another and to be able.

-last section we wrote an equation of a line using its slope and y-intercept -now, you will write an equation of a line.

Writing Equations in Point- Slope Form. Objectives Write the equation of a line in point-slope form. Write linear equations in different forms.

Graphing Lines Using Slope Intercept Form Algebra 1 Glencoe McGraw-HillLinda Stamper.

DAY 1 DISTANCE ON THE PLANE – PART I: DISTANCE FROM THE ORIGIN MPM 2D Coordinates and Geometry: Where Shapes Meet Symbols.

6-7 Polygons in the Coordinate Plane. Classifying Quadrilaterals Given the coordinates of the vertices, how would you determine if the quadrilateral is…

Notes Over 10.1 Finding the Distance Between Two Points Find the distance between the two points.

LESSON 20 PREREQ B: Writing the Equation of a Line.

The Distance and Midpoint Formulas

Midpoint and Distance in the Coordinate Plane

1-3 The Distance and Midpoint Formulas

Coordinate Geometry Notes Name:____________________________

Section 6.6 Polygons in the Coordinate Plane

Apply the Distance and Midpoint Formulas

P.5 The Cartesian Plane Our goals are to learn

Lesson 5-4 Coordinate Geometry

Lessons 4.1 & 5.5: Introduction to Triangles

6-4/6-5: Rhombuses, Rectangles & Squares.

Midpoint and Length Applications.

The mid-point of two points.

6.3 Proving Quadrilaterals are Parallelograms

Proving a quadrilateral is a parallelogram

Unit 5: Geometric and Algebraic Connections

The Distance & Midpoint Formulas

Bell work Algebra 2 1. Find ( f ⋅ g)(x) for f(x) =

Presentation transcript:

4.1/4.2 Distance, Midpoint, Slope and Equations Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations of lines Warm-up (IN) Find the length of the 3rd side of each triangle: 1. a=4, b=7 2. a=6.3, c=12.4 3. b=43.1, c=157.8 Solve for b: 4. 5. 6. 8.1 or 10.7 151.8 -3 4.5 17

Notes Given two points: Distance Formula - Midpoint Formula - Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations of lines Notes Given two points: Distance Formula - Midpoint Formula - Slope Formula -

a. Find the midpoints of the sides of the quad. Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations of lines Ex 1 – The vertices of Quad STAR are S(-1,4), T(3,5), A(4,1) and R(0,0). a. Find the midpoints of the sides of the quad.

b. Give the most specific name for STAR. Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations of lines S(-1,4), T(3,5), A(4,1) and R(0,0) b. Give the most specific name for STAR.

S(-1,4), T(3,5), A(4,1) and R(0,0) Rhombus?? Or Square?? Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations of lines S(-1,4), T(3,5), A(4,1) and R(0,0) Rhombus?? Or Square??

Find the lengths of the diagonals to see if the angles are right Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations of lines Find the lengths of the diagonals to see if the angles are right S(-1,4), T(3,5), A(4,1) and R(0,0) Right Square!!

Slope-intercept form of a line - Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations of lines Slope-intercept form of a line - y=mx+b slope y-int Ex 2 – write the equation of the line… a. With slope -3 and y-int -4 y= -3 x -4 b. With slope 4 and contains (-2,8) y=mx+b (-2) +b x +16 8= 4 y= 4 8= -8 +b 16= b

c. contains (-2,8) and (4,2) y=mx+b 2 -8 -1 (4) +b y= - x +6 -6 2= = = Learning Objective: to find the distance between 2 points, the coordinates of the midpoint, and the slope. To classify polygons by their side lengths and to write equations of lines c. contains (-2,8) and (4,2) y=mx+b 2 -8 -1 (4) +b y= - x +6 -6 2= = = -1 4 +2 6 2= -4 +b 6= b Horizontal lines vertical lines m=0 m=undefined y=# x=#

Out – None Summary – Today, I learned… HW – p. 169-170 #4,7,11,12 p. 176-177 #2,3,9-16